Our friends have a son who has asthma and allergies, but was able to spend time with a Yorkie without much trouble, so they got one. They kept it out of his room, and he washed his hands after playing with it, and he did fine.
Whatever breed you are interested in, have your son spend time playing with it, really get good exposure, and keep in mind that sometime allergic reactions can be subtle. I spent years denying that my DD was allergic to our cats (don't flame me, we had the cats first, and she was fine her first 4 years of life....) but once we tested her, she was allergic. Once the cats were re-homed, her asthma really changed.
Just to share our family's experience with allergies and pets
ne theory of allergies says that our bodies can handle only so much, and adding one little bit more causes overload (like the straw and the camel) and that is when we suffer. In my DD's case, she never had an attack because of the cats - but every time she caught a cold, she had to go on oral steroids to recover. She hasn't taken a single one since our cats have been gone. I guess my point is, allergies can be subtle!
Good luck, and I hope you find one that works for your family!