If the coyote is classed as vermin and your jurisdiction treats it as varminting (pest extermination) and not hunting, requirement for softnose expanding bullets may or may not be required. Most sporting goods counters locally carry wildlife resource agency booklets on hunting regulations, so ask, read and follow.
Personally, I think it would be difficult to tell the difference between a wound from a Full Metal Jacket 55gr-62gr 5.56x45mm and a soft point 45gr .223 Remington hunting round. Both are pretty explosive on flesh and bone. The softnose would be less likely to overpenetrate and on exit would be so deformed that it would not travel as far as a FMJ. Humane kills are possible with both, but I suspect a FMJ would travel further if it exited the coyote.
Remember, to anti-gunners, the FMJ are "armor piercing" and the softnose are "dum-dum bullets" and why do you need such awful bullets? Bullets need to be regulated so they are as safe as teddy bears, don't you know? Sorry for the thread drift.