Those that take Ephesians 5:19 and Colossians 3:16 to refer the Psalms are at least in good company in their folly, with a Perkins, an Ainsworth, a Manton, a Gill, an Owen, an Edwards, and a Murray. This has been discussed numerous times in this forum (do a search); below are a few quotations.
William Perkins (1558-1602), the “father of English Puritanism:” “[The Book of] Psalms contains sacred songs suitable for every condition of the church and its individual members, composed to be sung with grace in the heart (Col. 3:16)” (The Art of Prophesying, p. 14).
Henry Ainsworth (1571-1622), English Puritan, scholar in Hebrew and Rabbinics, commenting on Psalm 3: “There be three kinds of songs mentioned in this book: 1. Mizmor, in Greek psalmos, a psalm: 2. Tehillah, in Greek humnos, a hymn or praise: and 3. Shir, in Greek ode, a song or lay. All these three the apostle mentioneth together, where he willeth us to speak to ourselves with ‘psalms, and hymns, and spiritual songs,’ Ephesians 5:19.”
John Robinson (c.1576-1625), the minister of many of the Congregationalist settlers who journeyed to Plymouth Colony, New England: “What is required touching singing of psalms in the church? That they be such as are parts of the Word of God, formed by the Holy Ghost into psalms or songs, which many may conveniently sing together, exhorting and admonishing themselves mutually with grace in their hearts (Matt. 26:30; Eph. 5:19; Col. 3:16).”
John Cotton (1584-1652), New England Congregationalist theologian: “In both which places (Eph. 5:19, Col. 3:16), as the apostle exhorteth us to singing, so he instructeth us what the matter of our song should be, to wit, Psalmes, hymnes, and spirituall Songs. Now these three be the very titles of the Songs of David, as they are delivered to us by the Holy Ghost himself: some of them are called Mizmorim, that is Psalmes; some Tehillim, that is Hymnes; some Shirim, that is Songs, spirituall Songs. Now what reason can be given why the apostle should direct us in our singing to the very titles of David’s Psalms, if it were not his meaning that we should sing them? … The words of David and Asaph, as they were the words of Christ in the mouth of David and Asaph: so they were the words of Christ also in the mouths of the sonnes of Corah, or any other singers in the Temple.”
The Annotations of the Dutch Bible (1637) ordered and appointed by the Synod of Dordt (1618-1619) on Ephesians 5:19: “These three sorts of spiritual singing serve for one end. Namely to recreate the spirit; and are by some thus distinguished, that Psalms are all kind of spiritual songs, which are exercised, not only with the voice, but also with stringed instruments of music. Hymns, thanksgivings unto God, or metrical celebrations of God’s grace to us: and spiritual songs such indicting as contains all manner of spiritual doctrines. See also Col. 3:16, and these several names seem to be taken from the several inscriptions of the Psalms of David” (spelling modernized).
The Preface to The Bay Psalm Book (1640), the first book to be printed in New England: “… the whole Church is commanded to teach one another in all the several sorts of David’s psalms, some being called by himself Mizmorim: psalms, some Tehillim: hymns, some Shirim: spiritual songs. So that if the singing of David’s psalms be a moral duty and therefore perpetual; then we under the New Testament are bound to sing them as well as they under the Old: and if we are expressly commanded to sing Psalms, Hymns, and Spiritual Songs (Eph. 5:19; Col. 3:16), then either we must sing David’s psalms, or else may affirm they are not spiritual songs: which being penned by an extraordinary gifts of the Spirit, for the sake especially of God’s spiritual Israel, not to be read and preached only (as other parts of holy writ) but to be sung also, they are therefore most spiritual, and still to be sung of all the Israel of God: and verily as their sin is exceeding great, who will allow David’s psalms (as other scriptures) to be read in churches (which is one end) but not to be preached also, which is another end so their sin is crying before God, who will allow them to be read and preached, but seek to deprive the Lord of the glory of the third end of them, which is to sing them in Christian churches.”
Thomas Manton (1620-1677), English Puritan, commenting on Ephesians 5:19: “The learned observe, these are the express titles of David’s Psalms, mizmorim, tehillim, and Shirim, which the Septuagint translate, psalmoi, humnoi, and odai, ‘psalms, hymns, and songs,’ [and] seem to recommend to us the book of David’s Psalms.”
The twenty-six Puritan signatories of the Preface to the 1673 London edition of the Scottish Metrical Psalter: “… to us David’s Psalms seem plainly intended by those terms of ‘psalms and hymns and spiritual songs,’ which the apostle useth (Eph. 5.19; Col. 3.16)” (the signatories include John Owen, Thomas Manton, Matthew Poole, Thomas Watson, Thomas Vincent and William Jenkyn).
Dr. John Gill (1697-1771), English Baptist, commenting on Ephesians 5:19: “By psalms are meant the Psalms of David, and others that compose the book that goes with that name; and by hymns we are to understand, not such as are made by good men, without the inspiration of the Spirit of God; since they are placed between psalms and spiritual songs, made by men inspired by the Holy Ghost … but these are only another name for the book of Psalms, the running title of which may as well be the book of Hymns, as it is rendered by Ainsworth … and by spiritual songs are meant the same Psalms of David, Asaph, etc. and the titles of many of them are songs … These three words answer to Mizmorim, Tehillim, and Shirim, the several titles of David’s Psalms …”
Jonathan Edwards (1703-1758): “Another thing God did towards this work at that time was His inspiring David to show forth Christ and His redemption in Divine songs, which should be for the use of the Church in public worship throughout all ages. This was also a glorious advancement of the office of redemption, as God hereby gave His Church a book of divine songs for their use in that part of their public worship–viz., singing His praises throughout all ages to the end of the world. It is manifest the Book of Psalms was given of God for this end. David is called the “sweet Psalmist of Israel” (II Sam. 23:1), because he penned Psalms for the use of the Church of Israel; and we find the same are appointed in the New Testament to be made use of in their worship: ‘Speaking to yourselves in psalms and hymns and spiritual songs’ (Eph. 5:19).”
John Brown of Haddington (1722-1787), Scottish Presbyterian, author of the Self-Interpreting Bible: “The Holy Ghost hath, under the New [Testament], plainly directed us to the use thereof [i.e., of the Psalms], Col. 3:16; Eph. 5:19. The Psalms, Hymns and Spiritual Songs, there recommended, are plainly the same with the Mizmorim, Tehillim, and Shirim, mentioned in the Hebrew titles of David’s Psalms, 3, 4, 5, etc.; 145, 120, 134.”
John Murray (1898-1975), professor at Westminster Theological Seminary: “Paul’s usage will show that the word ‘Spiritual’ is derived from the Holy Spirit. ‘Spiritual words’ (I Cor. 2:13) are words taught of the Holy Spirit. The ‘Spiritual man’ (I Cor. 2:15) is the man indwelt and controlled by the Holy Spirit. ‘Spiritual songs’ (Eph. 5:19; Col. 3:16) are songs indicted by the Holy Spirit. ‘Spiritual understanding’ (Col. 1:9) is the understanding imparted by the Holy Spirit (cf. also Rom. 1:11; I Cor. 3:1; 10:3-4; 12:1; 15:44, 46; I Pet. 2:5)” (Epistle to the Romans, vol. 1, p. 254).
These and others are found at this link.
William Perkins (1558-1602), the “father of English Puritanism:” “[The Book of] Psalms contains sacred songs suitable for every condition of the church and its individual members, composed to be sung with grace in the heart (Col. 3:16)” (The Art of Prophesying, p. 14).
Henry Ainsworth (1571-1622), English Puritan, scholar in Hebrew and Rabbinics, commenting on Psalm 3: “There be three kinds of songs mentioned in this book: 1. Mizmor, in Greek psalmos, a psalm: 2. Tehillah, in Greek humnos, a hymn or praise: and 3. Shir, in Greek ode, a song or lay. All these three the apostle mentioneth together, where he willeth us to speak to ourselves with ‘psalms, and hymns, and spiritual songs,’ Ephesians 5:19.”
John Robinson (c.1576-1625), the minister of many of the Congregationalist settlers who journeyed to Plymouth Colony, New England: “What is required touching singing of psalms in the church? That they be such as are parts of the Word of God, formed by the Holy Ghost into psalms or songs, which many may conveniently sing together, exhorting and admonishing themselves mutually with grace in their hearts (Matt. 26:30; Eph. 5:19; Col. 3:16).”
John Cotton (1584-1652), New England Congregationalist theologian: “In both which places (Eph. 5:19, Col. 3:16), as the apostle exhorteth us to singing, so he instructeth us what the matter of our song should be, to wit, Psalmes, hymnes, and spirituall Songs. Now these three be the very titles of the Songs of David, as they are delivered to us by the Holy Ghost himself: some of them are called Mizmorim, that is Psalmes; some Tehillim, that is Hymnes; some Shirim, that is Songs, spirituall Songs. Now what reason can be given why the apostle should direct us in our singing to the very titles of David’s Psalms, if it were not his meaning that we should sing them? … The words of David and Asaph, as they were the words of Christ in the mouth of David and Asaph: so they were the words of Christ also in the mouths of the sonnes of Corah, or any other singers in the Temple.”
The Annotations of the Dutch Bible (1637) ordered and appointed by the Synod of Dordt (1618-1619) on Ephesians 5:19: “These three sorts of spiritual singing serve for one end. Namely to recreate the spirit; and are by some thus distinguished, that Psalms are all kind of spiritual songs, which are exercised, not only with the voice, but also with stringed instruments of music. Hymns, thanksgivings unto God, or metrical celebrations of God’s grace to us: and spiritual songs such indicting as contains all manner of spiritual doctrines. See also Col. 3:16, and these several names seem to be taken from the several inscriptions of the Psalms of David” (spelling modernized).
The Preface to The Bay Psalm Book (1640), the first book to be printed in New England: “… the whole Church is commanded to teach one another in all the several sorts of David’s psalms, some being called by himself Mizmorim: psalms, some Tehillim: hymns, some Shirim: spiritual songs. So that if the singing of David’s psalms be a moral duty and therefore perpetual; then we under the New Testament are bound to sing them as well as they under the Old: and if we are expressly commanded to sing Psalms, Hymns, and Spiritual Songs (Eph. 5:19; Col. 3:16), then either we must sing David’s psalms, or else may affirm they are not spiritual songs: which being penned by an extraordinary gifts of the Spirit, for the sake especially of God’s spiritual Israel, not to be read and preached only (as other parts of holy writ) but to be sung also, they are therefore most spiritual, and still to be sung of all the Israel of God: and verily as their sin is exceeding great, who will allow David’s psalms (as other scriptures) to be read in churches (which is one end) but not to be preached also, which is another end so their sin is crying before God, who will allow them to be read and preached, but seek to deprive the Lord of the glory of the third end of them, which is to sing them in Christian churches.”
Thomas Manton (1620-1677), English Puritan, commenting on Ephesians 5:19: “The learned observe, these are the express titles of David’s Psalms, mizmorim, tehillim, and Shirim, which the Septuagint translate, psalmoi, humnoi, and odai, ‘psalms, hymns, and songs,’ [and] seem to recommend to us the book of David’s Psalms.”
The twenty-six Puritan signatories of the Preface to the 1673 London edition of the Scottish Metrical Psalter: “… to us David’s Psalms seem plainly intended by those terms of ‘psalms and hymns and spiritual songs,’ which the apostle useth (Eph. 5.19; Col. 3.16)” (the signatories include John Owen, Thomas Manton, Matthew Poole, Thomas Watson, Thomas Vincent and William Jenkyn).
Dr. John Gill (1697-1771), English Baptist, commenting on Ephesians 5:19: “By psalms are meant the Psalms of David, and others that compose the book that goes with that name; and by hymns we are to understand, not such as are made by good men, without the inspiration of the Spirit of God; since they are placed between psalms and spiritual songs, made by men inspired by the Holy Ghost … but these are only another name for the book of Psalms, the running title of which may as well be the book of Hymns, as it is rendered by Ainsworth … and by spiritual songs are meant the same Psalms of David, Asaph, etc. and the titles of many of them are songs … These three words answer to Mizmorim, Tehillim, and Shirim, the several titles of David’s Psalms …”
Jonathan Edwards (1703-1758): “Another thing God did towards this work at that time was His inspiring David to show forth Christ and His redemption in Divine songs, which should be for the use of the Church in public worship throughout all ages. This was also a glorious advancement of the office of redemption, as God hereby gave His Church a book of divine songs for their use in that part of their public worship–viz., singing His praises throughout all ages to the end of the world. It is manifest the Book of Psalms was given of God for this end. David is called the “sweet Psalmist of Israel” (II Sam. 23:1), because he penned Psalms for the use of the Church of Israel; and we find the same are appointed in the New Testament to be made use of in their worship: ‘Speaking to yourselves in psalms and hymns and spiritual songs’ (Eph. 5:19).”
John Brown of Haddington (1722-1787), Scottish Presbyterian, author of the Self-Interpreting Bible: “The Holy Ghost hath, under the New [Testament], plainly directed us to the use thereof [i.e., of the Psalms], Col. 3:16; Eph. 5:19. The Psalms, Hymns and Spiritual Songs, there recommended, are plainly the same with the Mizmorim, Tehillim, and Shirim, mentioned in the Hebrew titles of David’s Psalms, 3, 4, 5, etc.; 145, 120, 134.”
John Murray (1898-1975), professor at Westminster Theological Seminary: “Paul’s usage will show that the word ‘Spiritual’ is derived from the Holy Spirit. ‘Spiritual words’ (I Cor. 2:13) are words taught of the Holy Spirit. The ‘Spiritual man’ (I Cor. 2:15) is the man indwelt and controlled by the Holy Spirit. ‘Spiritual songs’ (Eph. 5:19; Col. 3:16) are songs indicted by the Holy Spirit. ‘Spiritual understanding’ (Col. 1:9) is the understanding imparted by the Holy Spirit (cf. also Rom. 1:11; I Cor. 3:1; 10:3-4; 12:1; 15:44, 46; I Pet. 2:5)” (Epistle to the Romans, vol. 1, p. 254).
These and others are found at this link.