The Psalms are certainly inspired, but we have moved from the Old to the New Covenant. We no longer pray for the destruction of our enemies. Rather, as Jesus put it in Matthew 5:
“43 “You have heard that it was said, ‘You shall love your neighbor and hate your enemy.’ 44 But I say to you, love your enemies and pray for those who persecute you, 45 so that you may be sons of your Father who is in heaven; for He causes His sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous. 46 For if you love those who love you, what reward do you have? Do not even the tax collectors do the same? 47 If you greet only your brothers, what more are you doing than others? Do not even the Gentiles do the same? 48 Therefore you are to be perfect, as your heavenly Father is perfect.”
Or to put it with even greater clarity, from Luke 6:
“27 “But I say to you who hear, love your enemies, do good to those who hate you, 28 bless those who curse you, pray for those who mistreat you. 29 Whoever hits you on the cheek, offer him the other also; and whoever takes away your coat, do not withhold your shirt from him either.”
In this Covenant, we pray for God to bless our enemies. However, we are encouraged to pray to God to “deliver us from evil” - and I do so, every single day. (I.e.: you can pray that Obama & his family will be blessed, & even that they will know the greatest blessing of all, new life in Christ. It’s not inconsistent, however, to pray at the same time that God will deliver us from the evil Obama is inflicting. Both prayers can be answered, & are not mutually exclusive.)
The Old Testament moral law is God’s eternal Law and is not abrogated by the Covenant of Christ.
Matthew 5:17 “Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil.”
The Old and New Testament do not contradict each other in regard to imprecatory prayer and loving one’s enemies.
God called His people to love their enemies even in the Old Testament:
Proverbs 25
“21 If thine enemy be hungry, give him bread to eat; and if he be thirsty, give him water to drink:
22 For thou shalt heap coals of fire upon his head, and the Lord shall reward thee.”
The Psalms and Proverbs do not contradict each other.
In Matthew, Jesus is dealing with personal wrongs.
Those teachings to not contradict prayers that God gives to be prayed against His enemies.
One of the great heresies in America which took hold in the 19th century was the idea that Christians were supposed to stop restraining the most wicked sins against God and man based on the deceptive interpretation of Matthew 5. Such a heresy, after all, even would mean that a Christian must give up their right and responsibility of self-defense against criminals and attacks, which, of course, is nonsense.