That's a good question:
Dear friend, I imagine most, if not all of us have wished ill harm to someone or some group that we feel have done us or others wrong. I presume, because we are created in the image of God we have imputed in us a sense of justice in not wanting someone to get away with doing evil. In the Psalms we see David asking God to pour out his wrath upon evildoers. David prays vividly that the children of his enemies "be fatherless and his wife a widow. May his children be wandering beggars; may they be driven from their ruined homes" So after reading Psalm like 35, 69 and 109, most assuredly we would answer this question with a resounding "YES".
But fortunately when the Bible is taken in context and with study we know that this category of psalms are called (big word) an imprecatory (curse, invoke judgment) psalm. Simply meaning, while this is not a model for how we are to think or pray but are given for an example of moral indignation, not as a need for personal vengeance or vindictiveness. Instead they are prayers that keep Gods justice, sovereignty, and protection in mind.
Even though Romans 3:23 "for all have sinned and fall short of the glory of God." the first verse that came to mind when hearing this question Nevertheless, "Romans 5:6-10. Is clear in its example by Jesus "But God demonstrates His own love toward us, in that while we were still sinners (enemies), Christ died for us."
We all have a need for forgiveness. When we are enemies against God, He still forgives us and still saves us.
For Christian and non-Christians alike I believe Matthew 6:15, rings true, Christ has called us to forgive, for His word is true for all.
Concluding answer: No it's not alright to pray for ones destruction-Fun maybe, self-righteous definitely, but again, we are called to forgive one another. I admit forgiveness is one of the hardest things to do, especially when it happen to you or a loved one but as quoted by Dr. Rosalie de Rosset (Author of "How to pray" and "The imitation of Christ")
'"Forgiveness demands profound trust in the Lord who sees and whose justice is far more complete than any course of action we may long for."
I hope this was helpful, please leave a comment, I would love to hear from you again.
From My Heart page (Nov. 2016 archives)"Lessons learned while driving"
also ref: Luke 6:27, Colo. 3:13, Eph. 4:32, Matt. 18:21-22, and Prov. 10:12
"Truth of the word".