Hello from Georgia,
I once again find myself thinking outside the box. All of the rounds discussed would be sufficient to dispatch a coyote, but then again. so would a 45/70. I have found them to be as accurate as almost anything available, and certainly good enough to take smaller game at 200 yards. "overkill" some may say, but I have killed a bunch of coyotes and have never encountered one that was "to dead". There are some very good lower velocity loads that can start a younger hunter, and then there is room to work up to Grizzly Bear level loads. A smaller cartridge may serve well, but a 45/70 is so much fun, you should at least get a barrell to fit the .223 you get. This is just the views of a regular old country boy from Georgia who likes to flip coyotes.
Dave