You don't say how big your kid is. That said, for a young shooter or some small shooter's, recoil is more a matter of perception. The "bark" is related to the bite. Therefor the bite should be low as possible. If you handload, I'd suggest a 250 Savage if you could find one. If not then my second choice would be a 260 Rem. I've no experience with the 260 Rem but everyone say's it's just like the 6.5x55, which I do have experience with. Recoil is modest and bark is also. I would also not concern myself with getting a light weight rifle. Something around 8# will help reduce percieved recoil. And if you scope it, I'd go for a straight 4x scope. Their not all that expensive and you can alway's get something else as his abilities increase. Likely as not, get him a 3x9 at this point, and he'll wear out the adjusting ring!
Oh yea, one more thing, get at least a 22" barrel. Muzzle blast is also precieved recoil.