In my opinion, no single shot .22 is a good gun for squirrels. Squirrels can be hard to hit with a 12 gauge, why make your son have only 1 shot to kill it with??? Its hard enough with a .22 with a 14 shot tube magazine!!
If it is mainly for target shooting, then I would get a bolt action, and for hunting use, nothing but a semi-auto. Just start off out in one shell and not a clip, and then work up. Just make him respect the gun, and you will be fine. A .22 bolt action can work for squirrels, but is still to much hassel to jack in another shell after each shot. But for accuracy, nothing beats a BOLT action for TARGET SHOOTING!!
Just my .02