To rightly divide the Word of Truth requires serious study (2 Timothy 2:15), not to mention spiritual enlightenment (1 Corinthians 2:14). The passage to which you refer is undoubtedly one of severe imprecations. To begin to understand it requires an understanding of the time in which it was written. 

The psalm was written by David a thousand years before the birth of Christ. The Scripture teaches us that "God sent His Son" when "the time had fully come" (Galatians 4:4). The Old Covenant and God's giving of His Law was to prepare the world for the New Covenant and God's giving of His Son. Whereas the Old Covenant was all about the letter of the Law, which kills, the New Covenant was all about the spirit of the law, which gives life (2 Corinthians 3:6). A good example of this is found in John 8:1-11, where Christ in love—the spirit of the Law—saves a woman condemned—the letter of the Law—from stoning.

As an Old Testament man, David knew the letter of the Law. His condemnation of untoward things was not tempered by love. The only solution he saw to the enemies of God was their eradication, not their salvation, since he lived a thousand years before the Savior came.

Do you remember Christ's explanation for the permitting of divorce in ancient Israel? Our Lord explained how Moses' permitting of divorce was predicated upon ancient man's hardness of heart (Matthew 19:3-9). In other words, if men could not have divorced their wives they would have killed them. Thus, divorce was permitted to protect women in the ancient uncivilized world. 

From the very beginning, God always intended marriage to be a lifelong union between one man and one woman. However, it wasn't until the fullness of time had come that the world was sufficiently prepared for Christ to elevate marriage above the concept of the ancient uncivilized world to the divine idea. Today, Christians are to view marriage as a lifetime commitment. Nothing less is permissible. 

There is perhaps no better place to turn in the Scripture to see God's moving of the world from its ancient uncivilized past—Old Covenant and letter of the Law—to a new civilized Christian Era—New Covenant and spirit of the Law—than our Lord's Sermon on the Mount (Matthew 5-7). For instance, in the Sermon on the Mount, Christ taught that we are no longer to practice "an eye for an eye, and a tooth for a tooth," as King David did, but to turn the other cheek (Matthew 5:38-39). Furthermore, we are no longer to hate our enemies, but to love them; no longer to curse them but to bless them; and no longer to pray for their eradication, but for their salvation (Matthew 5:43-48). 

Obviously, in light of the above, it is not "righteous" for a Christian "to pray that an enemy's children be punished for their father's transgressions." Instead, the righteous thing for us to do is to pray for the salvation of both our enemies and their offspring. By doing so, we will prove ourselves to be the children of God, for only God's children are enabled by Christ to pray such prayers (Matthew 5:45-48). 

A final point should be made about the passage in question. It not only stands out because of its acid dipped imprecations, but also because it is used in the New Testament in reference to Judas Iscariot (Acts 1:20). Its harsh severity can therefore be attributed to the fact that it not only refers to King David and his foe, but also to Jesus Christ, the King of Kings, and His betrayer. In addition, it may have further and ultimate allusion to the other "son of perdition" mentioned in Scripture, the coming so-called antichrist (John 17:12; 2 Thessalonians 2:3).