Anonymous wrote:There are no GMO fruit trees, so any tree will fit your bill on that one.
Organic regulations are about pesticides and fertilizers. Most trees you buy aren't fruit bearing yet, so they haven't been treated with pesticides. If you don't treat the tree with non-certified-organic methods for 3 years (about the time it will take to start bearing fruit) it would in theory meet organic certification.
Actually there, namely papayas. But I doubt that OP is looking for a papaya tree.
OP, if you want a tree that you might not have to spray, try Liberty or Freedom. Remember that you need two different kinds of apple trees to get apples. Also, I have a Liberty apple tree, and if I really wanted to get apples from it, I would have to spray it with a sulfur or a copper fungicide, because the apples get cedar apple rust.