"All evangelicals pray for the salvation of individuals, fully expecting that the effective prayers of the righteous can accomplish much (Jas 5:16). But how can Arminians pray for the conversion of an individual person if God would have to override the free will to convert that person? The most Arminians could pray for would be neutral, nonthreatening things that do not infringe upon the 'rights' of the sinner.
Calvinists can happily pray for specific people to be converted, because they know quite well that if God does not in mercy intervene to free sinners from spiritual death, they will never be saved at all. God may have willed that particualar prayers will be part of the chain leading to a person's salvation. Prayer is both reasonable and effective, precisely because God is in control and can override the human will to answer them."
-R.K. McGregor Wright, No Place for Sovereignty p.193
Here is an example of a free-will advocate praying that God would 'cause' Calvinists to understand the truths of the gospel.