Crob00, you've got a good bit of friendly PM ribbing because the 243 is widely considered about the best killer before entering commonly accepted overkill for coyotes. I've used that exact round on a lot of ND coyotes (20&22" barrels).
The only time I've experienced what your describing is with poor shot placement. Poor placement doesn't necessarily mean an innacurate shot. You probably know a coyote's vitals are a good bit forward compared to most game but it was news to me when I got started. Make sure to aim right up the front leg, not behind like the classic deer placement that little bit makes a big difference. I have found if they are quartering towards you, even a little the varmint bullets can have troubles.
How your 223 did better is strange but there is always lots of factors at play in hunting conditions. Nothing much more frustrating than run offs! Coyotes are notoriously tough. My friend always jokes he's switching to a 300 Weatherby! I'd suggest really concentrating on that forward chest shot. Best of luck