What about a gun that my 12 year d would feel comfortable shooting as well?
Many years ago I read an article by one of my all time favorite hunting writers, John Wootters. The title was something like, "Seven (or it may have been eight) Deer Rounds to Start and Finish With." The idea was to name deer rounds a youth could start deer hunting w/, yet continue to use in adult hood. IIRC, he liked the 250 Savage, 7X30 Waters, 7-08, 6.5X55, 30-30, 300 Savage and possibly 260 Remington. Those are all fine guns. W/ the advent of factory reduced recoil rounds, I think one could reasonably add the 270 Win, 308 Win, 30-06 and 25-06. When faced w/ the same scenario years ago, I bought my 12 y/o son a 308 Win.
Use reduced recoil loads, have a nice recoil pad installed on the butt plate, me sure the stock fits him well, use ear muffs AND plugs at the range and consider using a "sissy" bag when shooting on the bench and your son should be fine.