It somewhat depends on your goal. I'd say if saving pelts it would be a 204 or 223. If hammering them I'd say a 22-250 or 220 swift and add a 243 if shots are long and it's windy. The latter becomes more versatile as you can shoot heavier bullets that are better suited for deer and hogs.
I'm shooting a 22-250AI with a 75 grain bullet, not gentle on pelts but it's a hammer on anything from a coon to a deer or hog at reasonable range. With the high BC bullet, it will hammer the yotes way out and buck the wind better than a 50 or 55 grainer. Only issue is you'll almost never find a factory rifle with enough twist to shoot the heavies in a 22-250.
I have shot lots of coyotes with 223, 22-250, 220 Swift, 243, 25-06, and a bunch of others. My main gripe on the Swift (and I shot a Swift enough to burn the barrel out of a Remmy 40XBKS), is the brass. Long tapered case and semi-rimmed case is a PITA for a reloader as far as I am concerned. But it sure kills good. Not really any better than a 22-250 though. Both are very efficient as far as killing.
But if you aren't saving fur, my absolute favorite is the 243. Barrel life isn't great, but neither is a Swift or 22-250. That 243 will flat lay coyotes down though. My favorite bullet is a 87 VMAX, really good BC for a varmint bullet. Bucks the wind pretty good, and it is flatter than my 6.5 Creedmoor to 500. That 87 opens fast and makes a mess. You get any kind of a good piece of them, and they aren't going to go far. Most are down in their tracks, not many spinners. Lots of folks like the 70 VMAX as well, and if you are just shooting 300 or so the 58 is a hand grenade. Not much is flatter out to 300.
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