Lots of good advice. I'd like to second Nomercy's point about the ear protection, though. A young shooter's first impression of a rifle will determine how they feel about it for a long time. The muzzle blast from a deer rifle hitting unprotected ears makes it seem like you're getting pounded no matter how light the recoil.

As so many said, a .257 Roberts or .260 Rem. would be great for a kid or an adult, carrying just a tad more insurance than a .243, yet still having very mild recoil.

If you can tell the difference in recoil between a .308 and .30-06 with the same bullet weights, you're more perceptive than I am. Some kids might shoot one of these just fine, but a lighter caliber seems like a wiser choice.