As far as shotgun vs .22 , we are limited to non buck shot size loads, I think #2's or #4's .. and I have rolled 2 coyotes with #2's and they both made it 100+ yards, 1 shot at 25 yards, the other at 35.

For the record I agree the .22 is not the best caliber, but I have shot several coyotes, 8 I think, with my .22, 1 of them wasn't recovered. I have found the velocitors to be an adequate round for killing a coyote, head on shots the center of the neck just below the jaw, and broad side shots through the vitals or where the head meets the neck. I use the same discipline I use in archery and hold off the shot till I know I have a good one. The 1 not recovered ran into a swamp, and I believe subemerged at least partially. It was a single shot through the vitals. 5 of those 8 dropped like a stone. 4 of them were spine shots through the throat, 2 kills were through the boiler room .. 1 of those were 3 through the chest. Except for the one which made a swamp, none travelled more than 20 yards.

I also hunt with a .223, and to be honest, have seen almost the same exact performance from the .22 in lethality as the .223, just the range of the hunt is much greater. I don't think it is accurate to say that a .22 is not enough gun for coyotes, I think the real answer is that some hunters are not capable of being lethal with a .22. They either can't limit themselves to shots within a certain range, or do not take the time to become pin point accurate with their weapon. Those people should not use .22's as they require more room for error due to either lack of patience, discpline or shooting ability. Not bragging, but I lack none of those qualities and find the .22 a very efficient coyote killer.

My point is not to advocate hunting with .22's, but if you are stuck with the choice between a .22 and a shotgun, and can hit a quarter 10 out of 10 times at 50 yards, and will pass on marginal shots .. don't think for a second you can't hunt and kill coyotes.