RE: Coyote gun
It's not thata 20 gauge is too light, it's that it is really limited on range.Any single projectile roundwill kill a coyote at 40-50 yards. In yourcaseI would recomend slugs, they'll give you more range than any buckshot configuration.
On thing you have to consuder in your setup is that a 222 is a great long range weapon and the 20 is a good short range gun, so if you go and put a big, fixed power scope on the gun and zero in at 250 yards, you're gonna have a big 'void' from say, 50 to 125 yards. if you're not going to put a scope on it at all, or keep your shots under 200, you're ready to go.