The inherent cruelty of predator/prey relationships is no rationalization for me to be deliberately cruel myself. I always try to kill the things I must kill, as cleanly and humanely as possible. One of the ways I try to ensure that will happen is by choosing a cartridge for hunting any given animal that will have enough power to always kill cleanly, humanely, and decisively if I behave properly.
I have shot enough coyotes that I have come to believe they are, pound for pound, one of the toughest animals I hunt. I have seen them, sometimes with horrific wounds, run a long way before falling, and I have tracked animals, that really should have died quickly, long distances before finding them. Sometimes, I have actually lost animals I knew I hit. I have used the .22RF when unexpected opportunities on coyotes presented themselves (only three times I can remember), and, because those chances were always very close ones, I was quickly successful with that round ... so far. But my experience with the rim fire certainly makes me think the cartridge is not what I would call "decisive" even at short ranges.
I think the .223 is the minimum round suitable for deliberate hunting of coyotes.