You didn't mention the caliber of gun he is shooting. Is he overgunned, or does he have a flinch? If not he needs to practice shooting at lifesize paper deer targets in the off season. This will improve his accuracy and help him concentrate on the vitals.

I used to have the same problem with buck fever. After killing a few deer it has really slowed down a lot. Also, I used to put the scope on every deer that came into range and pretend to shoot it. I made absolutely sure the safety was on, and my finger was away from the trigger. This helped greatly.