What POSSUM said... ^^^
Use a monolithic bullet (solid copper), Barnes TSX/TTSX or Hornady GMX.
These bullets can be used on both ungulates and coyotes with great success.
Although, I did buy a .223 earlier this year to help reduce the possiblity of or atleast the size of exit holes.
My .243 liked 58gr Vmax @ 3900-4000 FPS... This was destroying the dogs & fur at anything less than 300 meters.
I recently modified & rebarreled the .243 for PRS sytle shooting, so coyote duty is relinquished to the .223...