I've struggled with this very issue myself. After much soul-searching, I've come to the conclusion that there is nothing "wrong" about asking God to change someone's heart, He's in the business of doing that, after all...
However, it must be done the right way. You have to realize that you don't know everything about the situation and the future, and that you may be wrong regarding your interpretation of what His intentions are in this matter. Even if you see tremendous greater good that could possibly come from this relationship (a fuller conversion on his part, for example), it doesn't mean that you're necessarily correct, that there isn't an even greater, greater good God has in mind, or that the man will ever respond to even the most earnest entreaties from God in his heart.
All that said, if you believe that God has put this man in your life and in your heart, and you don't believe He's called you to stop praying regarding this, then by all means pray. I will pray for you as well (and I ask that you keep me and my own intention in your prayers, too). Listen to God's voice in you...He will tell you if this is a time to stand and persist or a time to let go and stop praying. In my own family and circle of friends, I seen five near-miraculous conversions of heart - marriages, relationships, healed friendships, and the like. Yes, people make their own decisions, but God can certainly guide and inspire us in our actions, emotions, and perspectives, and I don't see anything wrong with asking Him to do so (as long as it's done in good faith and appropriately).
While undergoing my own spiritual evoution regarding a similar situation, I've come to understand the following "tips":
1) don't make an idol of the other person (make them so important they consume your every thought and desire)
2) don't make an idol of the relationship you desire with the other person (making it so important it consumes your whole being, or you treat it as an end in itself)
3) don't make an idol of not being alone or of being married (same caveats as #2)
4) ask God to touch the other person's heart and help them fulfill the role in your life that He desires for them (and vice-versa)
5) ask God to soften both your hearts to the workings of the Spirit
6) ask God to change them and change you
7) ask God to remind the other person each day of the best and most attractive things you have to offer and that have been part of your relationship in the past (whether or not they find themselves inspired to see you in a different light will be entirely up to them)
I've found this article somewhat inspirational. Sometimes, God is waiting for us to surrender to Him before he answers the prayer (this definitely happened in two of the five examples I mentioned above). Not surrendering in order to get it (because that's not really surrendering), but really, truly, giving it to Him. It's very hard to do, and I'm not quite there yet with my own situation, but I know I will need to get there eventually...I pray for that, too. "Lord, help me to want what You want..."