My goodness its getting exciting here in the equipment forum today! I tripped on the knotted panties as I came in.
Let me add to this brush fire; your all just as wrong as you are right, I mean its a damn dog, not the hound of the baskervilles. They can literally be killed with any thing from a fork to a Buick, so whats the big deal? The whole question almost seems stupid were it not for the thrown in criteria at the end of the OP. Any of the calibers mentioned here will all work fine for killing coyotes, as to how well at what distance is up to the gun, the shooter, the ammo, the wind, the atmosphere, your Wheaties intake, and whether the stars aligned last night.
A far better and harder to answer question would be; What IS'NT a good coyote caliber?
If bullets come out the barrel, and you can consistently hit coyote sized targets at your intended ranges, then you have a coyote gun. I use whatever gun I happen to have on me, typically my DTA, and any of the barrels work great on coyotes. I may have not shot 37 recovered coyotes this year, and I probably wont shoot 37 next year.....probably wont see 37 coyotes by then either. But Shooting coyotes is like shooting anything else, practice, and be ready, and you'll get him.
Whats the big deal about this fur friendly business? so you wanna shoot some fatassed, high speed, flat shooting cartridge like a 22-250 or a .243, and then want it to delicately sneak through the hide and kill him? WTF?
Just shoot the damn thing and enjoy it. "Oh no, my pelt has a hole in it..." Yes, and ticks, flees, mange, shit, hair, eyes, claws, earwax, bits of bone, you name it. Its just a hide. Give it some character so the braves down to the trading post will have somethin to talk about after you leave.
I plugged me a nice little yote a while back, right at 500 yds. He didn't wanna come any closer, and I sure as fuck wasn't in the mood to crawl out to him, so I just shot him. No super flat wizzbang caliber with fur protecting bullets. Just a crummy old .308win, shooting 175smk's. And wouldn't you know it, he tipped right over after a single shot.
And not a noticeable hair was damaged......