.223 is fine for coyotes, IMO. I'd use an expanding bullet, though, which would not only be more likely to give you a clean kill but would also probably not make an exit hole in that pelt you want to sell.
A fellow up here says he has killed quite a few wolves with .223 and is partial to the Barnes bullet for that job. A big wolf will go way over 100 lb. So, with the right bullets and accurate shooting, it'd be just fine for 'yotes.
ps: A lot of coyotes will take a lot of deer. Just sayin'....... Choot 'em!