There are a number of references to confirming versus converting ordinance. I'm not sure where to find the exact terms "confirming grace" versus "converting grace," but the concept is certainly present (and the terms "confirming grace" and "converting grace" can be found being distinguished in other contexts).
Thomas Boston (from the portion I linked earlier)
"The difference betwixt the two former [i.e., the difference between the word and sacraments as means of salvation] is,
That the word is the mean of conversion, and the sacraments means of confirmation: so the word is the leading, and the sacraments are the subsequent means of salvation. The word is first to have its effect, then the sacraments have theirs on the soul, 1 Cor. 3:5 with Rom. 4:11."
David Dickson's Truths Victory over Error
"Are all that are baptized, undoubtedly regenerated?
No....
Because, Baptism is not a converting, but a confirming Ordinance, even as the Lords Supper is.
"
http://www.monergism.com/thethreshold/sdg/dickson/Truth's Victory Over Error - David Dickson.pdf
From Gillespie's
Aaron's Rod Blossoming
"[T]he word is not only a confirming and comforting, but a converting ordinance...whereas the sacrament is not a converting, but a confirming and sealing ordinance, which is not given to the church for
the conversion of sinners, but for
the communion of saints."
"Our divines hold that the sacraments are appointed of God, and delivered to the church as sealing ordinances,--not to give, but to testify what is given,--not to make, but confirm saints. And they do not only oppose the Papists'
opus operatum, but they simply deny this instrumentality of the sacraments, that they are appointed of God for working or giving grace where it is not."
p. 229
"Ursinus speaks so fully and plainly for us that none can say more. He distinguisheth between the word and sacraments, as between coverting and confirming ordinances, and argueth that the sacraments do not confer grace, because we receive not the thing by receiving the sign, but we get the sign because it is supposed we have the thing; yea, he speaks of it as a principle known to children." p.230
"I answer, That exhibition which they speak of, is not the giving of grace where it is not (as is manifested by the afore-quoted testimonies), but an exhibition to believers—a real, effectual, lively application of Christ, and of all His benefits, to every one that believeth, for the strengthening, confirming, and comforting of the soul. . . Our divines do not say that the sacraments are exhibitive ordinances, wherein grace is communicated to those who have none of it, to unconverted or unbelieving persons. . .
Protestant writers do not only oppose the opus operatum and the causalitas physica and insita but they oppose (as is manifest by the testimonies already cited[ix]) all causality or working of the first grace of conversion and faith in or by the sacraments, supposing always a man to be a believer and within the covenant of grace before the sacrament, and that he is not made such, nor translated to the state of grace in or by the sacrament."p.230
"Waleaus asserteth, both against Papists and some of the Lutherans, that sacraments do instrumentally confirm and increase faith and regeneration, but not begin nor work faith and regeneration where they are not."p.232
p.235-236
Stephen Marshall
"And after a needlesse shewing that you have read these Authors, you grant as much as I contend for, That the taking away the heart of stone, and infusing of a principle of new life, is only Gods work; and that a new heart, faith, &c. are the effects of
converting grace, and that in these things wee are passive: in summe, you are of my judgment in this point, that Infants are capable of new life, and some of them partakers of it: and I likewise consent with you, "
(
https://quod.lib.umich.edu/e/eebo/A89563.0001.001/1:4?rgn=div1;view=fulltext)
Thomas Manton (in a non-sacramental context)
"As soon as joined to him as our head, his grace is applied to us by his Spirit. It is first applied by converting grace, and then continually supplied by the confirming grace of the Spirit"
(
https://books.google.com/books?id=cJo_AAAAYAAJ&dq="confirming grace" "converting grace"&pg=PA389#v=onepage&q="confirming grace" "converting grace"&f=false)
(From one of the historical articles I linked by Ramsey.)
"Confirmation and conversion are two distinct functions, and so confirming grace is to be distinguished from converting grace. Although, as Richard Vines granted, confirming and converting grace may be the same in substance, even as every degree of heat is of the same nature as the first degree, there is still a difference between first coming to Christ and being strengthened and confirmed in Christ. Since the Word fulfills both functions, it is feasible that a sacrament could do so as well. Nevertheless, if baptism is divinely designed for sealing and confirming then one key implication would be that it is not a converting ordinance because sealing and confirming presuppose the existence of that which is being sealed and confirmed."
Richard Vines can be found here distinguishing between confirming and converting grace in relation to the sacrament:
https://books.google.com/books?id=1UssCf8Y6_YC&lpg=PA224&ots=YGrIs4SCs4&dq="confirming grace" "sacrament"&pg=PA224#v=onepage&q="confirming grace" "sacrament"&f=false