In my experience, coyotes are pretty much like geese: Have seen them killed cleanly at 30 yards with #6 lead shot, But as the range increases the density of the pattern (and shot itself) makes a considerable difference.
But good to know the problem is so complex.
Top of the morning to you John, I hope that this Columbus Day long weekend finds you and yours well. I'll add a Happy Thanksgiving to you both too from this side of the medicine line as I know you've traversed that near invisible 5 strand fence a few times!
Way, way back in the pre-ethernet days, we had to make do with VHS tapes and good old fashioned experimentation to figure out the vagaries of life.
We'd just started calling coyotes and deer - the deer part was really controversial with some of our fellow hunters as many assured us deer were mute and thus calling absolutely would not/could not work... but that's another story.
Anyway when we'd become reasonably proficient at regularly calling in coyotes, my best buddy and long time hunting partner announced he intended to shoot one with a shotgun - in the name of science of course. Again if faulty memory serves he might have seen some chap doing that on a cable TV show, but maybe that was after too, I can't say at present.
For armament, he chose one of his trusty Cooey 84 single shots, this one a 12 gauge with 3" chamber. We then rifled through our collective supply of 12 gauge shells, which I might add was not particularly unimpressive as we used to hunt ducks, upland game and since I'd always used a Lakefield Mossberg pump for our camping/shoo bear tool there was a selection of various slugs and buckshot.
My opinion was that we should use #4 buck since I'd used it for years at the start of my annual Hunter Safety class shooting a metal 5 gallon bucket of water at 20-25yds - which if one hasn't done that is often rather spectacular and leaves a life long impression on one's students.
However since it was his idea and his shotgun, I was outvoted and he chose some 3" steel T size shot, which I must admit patterned really, really well out of the little single shot. Recoil from that load I should add, appeared to this bystander as "sporty" at very least.
So it came to pass that one fine still morning in December I manned the call, of course with my usual coyote rifle - a custom 12lb, 26" heavy barrel .22-.250AI - sitting across my knee ni the event that a coyote might "hang up" too far out for the shotgun and need to be removed before it educated it's fellow dogs about camouflaged bushes that had evil intent.
On this particular morning however, the coyote in question had read the script and came in to what I recall was maybe 25 yards and buddy hit it coming toward us in the center of the chest.
The interesting thing to me while conducting the postmortem findings was that while none of the shot exited, it had broken nearly every bone from the chest rearward. I can only describe it as picking up a skin bag where the structure was gone and even the major leg bones at the top were no longer factory original shape.
While we'd seen that a couple times with chest shots with frangible bullets like the 55gr V-Max or Ballistic Tip which were 3800fps more or less from the .22-.250AI, it was remarkable enough that I clearly recall that detail all these decades later.
Anyway John, since clear memories seem to be remarkable for me anymore, I hope it's okay that I shared it with you and the rest of our fellow 'Fire coyote shooters.
All the best to you on your remaining hunts this fall.