I would get a good 22LR, You can buy 500 rounds for under $10 and you and your son can shoot all day. A CCI Velocitor has a 40gr gold dot hollow point traveling over 1400 fps that will kill anything coyote size and smaller. I read that the 17 HMR does not have very good penetration with the Vmax bullet because it explodes and was only sutible for varmints smaller than wood chuck.

I love my Ruger 77/22LR and it shoots every type of ammo very well, except the stingers. The Velocitors will shot a 1/2" at 50 yards.