As others have mentioned, try to find a rescue. Go to your local shelter and see what they have. They will give you a chance to be in the room and see how you, your son, and the dog get along. Find a bond, take it home.
Be careful with the puppy idea. They are cute, yes, but they are also a handful. They have a lot of energy in very small bursts, and they'll also go through the phase of trying to chew on things, including hands and fingers, which may be intimidating for someone who's hesitant with dogs.
Just a thought, but we have an organization near us (
https://muttville.org/) which specializes in senior dogs. There's probably somewhere similar near you. This may be a good move. They are generally well trained already, and more docile. Because everyone thinks they want a puppy these poor pooches get overlooked, but they need love too, and are super loving and grateful when someone gives them a home.
The disadvantage, being older dogs, is that they won't last as long and that you have a shorter time before the possibility of medical expenses crops up.
Still, think about it. You may be able to help your son and a 'senior' dog