.243 Win, 7mm-08, 6mm Rem (if you can find one), .257 Roberts, and he might even do ok with a 25-06.

Another suggestion I'd make, since it's his first time out this year, you might want to consider letting him use your .30-06, but load it with the Remington Managed Recoil ammo. It uses a 125gr bullet at 2600fps, making it kick about like a .243 Win. The 125gr .308cal bullet is a Core-Lokd bullet specially designed to perform at the reduced velocity, and is said to be quite effective on deer. I don't know what your situation is, but if getting him his own gun right now is less than do-able, it'd be a good option. Also, you might also consider getting him a rifle in .308 Win and still starting him on the Managed Recoil ammo. A couple-three years down the road when he's a little older and bigger he could work up to full-power ammo. The .308Win is great for everything up to elk and will serve him well for all the hunting he's likely to do for the rest of his life, unless he gets the wild hair to go after the great bears or large African game someday.

Good Luck to you and your son.

Mike