I started loading Hornady 30 cal. 150 gr, SST low recoil bullets for the kids years ago when they started hunting.
With the light bullets, both 30-06 and 308 are more than capable for deer out to 80 yards. The only times the bullets haven't passed clean through are when they hit a shoulder, or a rib bone on the way in and another rib bone on the way out.
Many other deer and moose have been taken with the same bullets, over a full powder load, out to 400 yards. If you make a clean shot, you have no worries, and no deer hearts to eat.
If you are only shooting to 30 yards, consider using a bow and arrow.