243 would be good, but here in our state, we can use anything 30 caliber or smaller for coyotes. Frankly, so far, I have not been very impressed with the anchoring power of the .223 for coyotes, and usually use my Browning Blr .308, and sometimes my 25-06 or even a model 94 30/30.
I do have a 22/250 in a Browning BLr, that I purchased for coyote hunting but I have not yet, taken a coyote with it. But on hindsight, I would probably be just as happy with a .243