It has never crossed my mind one time that .223 Rem could not kill a Coyote effectively.
My thinking would be to change bullet types.
I have ended up having to track every single yote I have shot with a .223, these are shoulder, stomach, and hind leg shots. I have seen them run with their intestines dragging behind them, and my partners and I can only boil it down to the areas we hunt must be somewhat trafficked by other hunters, and the yotes are familiar with the sound of a gunshot; adrenaline kicks in and they are gone. My partner shot a coon with a .223 and we had to track for a half a mile. Finishing it with a .45 to the head was satisfying.
.223 is feeling more and more like a peashooter to me. It certainly will kill a coyote, but it has no knockdown power. I'm looking for something to coyotes what a .223 is to rabbits