well, if they like walks but might not want a dog with a lot of energy and power (it could be dangerous for them until they are fully trained), a smaller breed is probably the best option.
poodles, papillons, cocker spaniels, corgis, shih tzu, and bulldogs (or mutt mixes of similar smaller dogs) would likely train up the fastest, though depending on the breed/mix/type they could have grooming needs that can be fairly intrusive.
more than anything, it comes down to the individual dog itself. If ever there's a situation where your parents might want a dog, do your best to convince them to adopt, and they might find a better fit on their own regardless of breed.
