I would try finding a used recurve in good shape that pulls about 35 pounds at 28", since you're on a limited budget. Not that there's anything wrong with the bows mentioned above, but if you need something less expensive, I wouldn't hesitate looking for a used bow. It's not at all unusual to find one for around a hundred bucks or less.
At a short draw length of around 23", that puts his holding weight at around 20-25# with a 35#@28" bow. I would look for a bow about 54" to 58 or 60" maximum AMO bow length since he is likely to be relatively short compared to an adult.