I have tried to deal faithfully with curses in the Psalms, for example, in a sermon on Psalm 69.

Psalm 83, however, presents a different challenge. At the end there is a strange mixture of supplication and imprecation:

Fill their faces with shame,
that they may seek your name, O Lord.
Let them be put to shame and dismayed forever;
let them perish in disgrace, 
that they may know that you alone,
whose name is the Lord,
are the Most High over all the earth.
(Psalm 83:16-18)

Imprecation: The word “forever” in verse 17 is a prayer for utter and eternal defeat: “Let them be put to shame and dismayed forever.”

Supplication: But the phrase, “that they may seek your name, O Lord,” is a prayer for conversion: “Fill their faces with shame, that they may seek your name, O Lord.”

It is true, as Kidner points out, that there is “fruitless seeking”. But it would be very strange that the psalmist would be praying for “fruitless seeking.” If that’s the prayer why not just pray that they not seek the Lord?

I think David Dickson is right:

If any of the enemies of God’s people belong to God’s election, the church’s prayer against them giveth way to their conversion, and seeketh no more than that the judgment should follow them, only till they acknowledge their sin, turn, and seek God.... For the rest of the wicked, irreconcilable adversaries, when shame of disappointment and temporal judgments are come upon them, the worst of all yet followeth, even everlasting perdition. (Commentary on the Psalms, Vol. 2, 67-68)