The 7mm-08 Rem is a good suggestion, but make sure the rifle isn't too light or there will be noticeable recoil with a 140 grain load. I have a Ruger 77 Mk II Lightweight and I can tell when it goes off. Now using a 120 grain bullet would help. I would also look into the 260 Rem as it is a fine compromise between the 243 Win and the 7mm-08 Rem. The 250 Savage and the 257 Roberts were mentioned and while not widely used anymore these are both fine deer cartridges with mild recoil. The 243 Win is nothing to sneeze at either when it comes to killing deer and it too can be had in several youth model guns.