We had a coyote problem back home when I was a kid, and I can personally testify that a .22 ain't gonna do it. You might get lucky with your shot placement, or it might succumb eventually, but you don't want a pissed off, wounded coyote wandering around your property.
Our firearm of choice was a Mini 14 with a 3x scope on top of it; it was a reliable round, and we could cover the chicken coup from the back deck of the house about 150 or so yards away. Only trick to shooting .223 is you have to be REAL careful about your backstop - make sure that round is hitting dirt if it misses or goes through the animal. Otherwise, your AR should be ideal.
Other option is the 12 gauge - less range, but it'll definitely work if you can hit the thing.
We also liked to keep the .223 around because we had mountain lions to boot...
Our firearm of choice was a Mini 14 with a 3x scope on top of it; it was a reliable round, and we could cover the chicken coup from the back deck of the house about 150 or so yards away. Only trick to shooting .223 is you have to be REAL careful about your backstop - make sure that round is hitting dirt if it misses or goes through the animal. Otherwise, your AR should be ideal.
Other option is the 12 gauge - less range, but it'll definitely work if you can hit the thing.
We also liked to keep the .223 around because we had mountain lions to boot...