If accuracy is the primary concern, one would get a .222. But suitable accuracy and suitable power are both required. You don't want to give up too much power to gain a tiny amount of accuracy.

FWIW, I hunted a lot of coyotes with .222, .223, and .22-250. I don't consider any of them to be a good coyote round; the .22-250 is the best but not by much. A .243 or 6mm works far better for that size game. The .22's deliver some spectacular kills but will also deliver some spectacular failures.