C.M.
I think young kids are automatically "me" centered so that's not odd. However, we do say that God does not grant wishes, and I like that you compare it to a genie. God is not going to make sure you get a certain present or help your team to win. God is there to give strength, wisdom and guidance. So when we pray we pray for those things--strength, wisdom and guidance. We don't pray for "things" like new bikes or trips to Disney World.
We always did it by saying that if you want someTHING, then you should either say "I wish for a new bike," or pray to God for guidance on how you can EARN a new bike. Gentle correction is all you need when they are young.
It depends on your beliefs, but we believe that God works through people, so if someone was sick we'd pray to God to make the doctors strong and smart to help heal them. I have heard my daughter pray that God help her parents to be strong and smart so we can earn money to buy her a new bike for her birthday. I think that's cute, and as our children grow older they will learn from examples on how to be caring toward others and less self-centered.
I also can't help but think that God must smile at the wishes of a young child. And sometimes He grants them, my daughter prayed that we be strong and smart enough to make money to buy her a new iPod Touch for her birthday, and I stumbled on a great deal on a refurbished one! We would have never been able to afford if if I hadn't found that deal. So who says God doesn't listent to the wishes of little children??