My 8 year old son hunted with my Savage 116 in .270 Winchester with the Remington Managed Recoil loads this year...
I broke him in slowly at the range starting him with a .22LR and 4 inch balloons...after "calling" his balloon color and breaking it from 25 yards I moved him to 50 yards...when he cleaned the rack of balloons at 50 yards...I switched him to the .270...
I will admit that it drew looks at the range...in fact everyone stopped and watched him happily call out the colors and mow down the next set of balloons...
The managed recoil .270 loads have no more recoil that the .243 and hit harder through 200 yards (though I limit my son to 50 yards for now)...as he gets older and can handle more recoil, I will move him up to the full power 130 grain loads...
Though I am considering getting him a Ruger M77 Compact in .308 and managed recoil loads for it...