RE: coyote shotgun
I have used everything from 6's to double ought buck. The trick with killing a coyote with a shotgun is to use the smallest shot that will reliably penetrate the skull, and go for the head/neck shot. This is usually 2's or BB's; although 4's will work at fairly close range. A body shot with 00 buck is going to kill the coyote eventually, but often not soon enough to facilitate recovery. These are amazingly tough critters!