This summer, I ran through a couple boxes of buck shot and #t's in my [beeep] gun looking for something that would knock coyotes down.
Forget about 4 shot, its not worth anything. You can kill them, though the ranged will be very short. Save it for shooting ducks, and get some proper shot for the coyotes, a couple boxes of buck shot won't set you back to much, I'd bet its about the same price per shot as good 4 shot.
It took me a while to figure out, but a good choke tube will pattern most any shell well. Really, last year I would have said, get 4 boxes of shells and pattern them. Now I'm of the opinion that you should get a good choke tube, and the cheapest boxes of shells.
Personally I use federal 4 buck, the cheap stuff. It patterns well out of my set up, can be found easily and is cheap to buy. Premium stuff like "dead coyote" rounds work better at long ranges, but my hunting style doesn't call for 50+ yard shotgun shots.