I've had FANTASTIC success w/ .223 Rem on deer the past couple of years. Just have to ensure proper bullet construction. Winchester makes a good 62gr deer load if your sticking to factory ammo. Nosler 60gr Partitions are hard to beat, but I don't know of a factory load w/ this bullet. Either way, they work fine as long as shots are in the chest cavity SOMEWHERE. I actually prefer forward shoulder/ low neck shots as the deer have yet to take another step w/ shots in this area. I tried some farther back (high lung shot aft of shoulder but still fwd of the diaphragm) for experimental purposes and can't tell any difference from the 30 cals. Its quite amazing! (Actually DEVASTATING was my impression- 20" bbl rifles run the velocity up enough to liquify the lungs- they've all sloshed when moved!)
If your boy can shoot well under pressure I reckon most any caliber will work given proper bullet construction, but 223 and 243 have less recoil than most rounds so it may make him a better shot.
BTW I'm now using a well constructed 55gr bullet that stops 'em like nothing I've ever seen. Scary!