First, an FMJ may not be legal to hunt with. Assuming that in your area the are, they are still not a great idea. Coyotes may be hard to hunt but they aren't hard to kill. Pick any center fire caliber you feel comfortable with and put the bullet where it needs to go.
As far as using a 155 grain amax on a coyote, it will kill it grave yard dead. Just be ready for large exit holes. The last time I saw a coyote shot with a 30 caliber amax the damage was not fit to post on a public forum.
If you don't hunt fur, "run what you brung" and start whack'n dogs. If you want to save the hide, My vote is for a 223 and a 50 grain vmax or nosler ballistic tip.