I'd like to interject here- I use #4 buckshot for coyotes, and it certainly works well, but I only use it because I can't find ay other non-steel large shot without going to 00 or 000 buck (and those are too big to reliably land pellets where you need 'em).
I just wanted to say, use fairly large shot (BB, BBB, T, F, #4 buck), use heavy shot (lead, hi-density, tungsten, bismuth, whatever), but for Heaven's sake DON'T USE HEVI-SHOT DEAD COYOTE.
Why?
Because I don't care how good a shotshell is, nobody should ever ever ever ever ever pay $5 PER SHOT for a 12 gauge. Simple.