I shotgun for coyotes in Eastern Washington when the pelts are prime. A shotgunned yote is a lot easier to stitch than the exit wound from any of the popular rifle calibers. If your just wanting to put the smack down on them then yes your 20 gauge will work but you'll need to get them into your lap. Investing in a good dead-dog choke will improve performance a lot. I use 12 gauge 3 inch #2's and I can reach them consistently at 60 yards. Anything past that is possible but you risk a long track.