Israel was a nation and as such had national enemies. She prayed, understandably enough, for the destruction of her national enemies. This is the central part of the prayers of imprecation.
The church of the new covenant is no longer a nation (an ethno-political, geographically located and identified entity). Rather the church is found among all nations and is that body of believers and their children who profess the true religion.
No part of the Bible is inappropriate for us as Christians as the whole Bible is the Word of God. However, everything in the OT, which pointed forward to our time, is now understood and interpreted in fulfillment. So when we as Christians pray the prayers of imprecation we do not pray for the destruction of the church's national enemies for, as noted above, we have none. We certainly have enemies of the cross and of our Lord, but they are not political enemies, because the church has no national and political identity.
When we pray imprecatory prayers with respect to the enemies of the cross, we pray that, as happened with us, they are destroyed as enemies and reconstituted as friends. In other words, to pray imprecatorily for the world is to pray that the world would be converted, ceasing its hostilities against the truth, repent, and become children of God, as we have become. As to ourselves, the imprecatory psalms serve as a prayer for our sanctification as we pray for the destruction of the devil and the flesh.
Paul tells us how we are to pray for rulers, in fact, for "all people," praying that we may lead peaceful and quiet lives. We ought to pray in this way because "this is good, and it is pleasing in the sight of God our Savior, who desires all people to be saved and to come to the knowledge of the truth" (I Timothy 2:1-4). One might say that the OT prayers of imprecation are taken up and transformed in this way in the NT and this is how we are to pray for all those about us, including our leaders. We do not pray for personal and national destruction any longer but for the salvation of the nations. We "Honor everyone," including "the emperor" (I Peter 2:17).
I am not suggesting that the President is equivalent to the emperor or king (supreme earthly ruler). But he clearly is a ruler, along with others, whom we should honor and for whom we should pray. We should pray in the way that Paul and Peter instruct us to pray for our rulers (and for all). In so praying, we take up everything that the imprecations of the OT ultimately signified, the salvation of the nations through the person and work of Jesus Christ (Matthew 28:18-20).
Peace,
Alan