When it comes to 223 I like Sierra 55 gr HP bullet #1390.
I just shot a coyote yesterday evening, a good strong 200 yard shot with the above listed bullet.
Bullet placed in the boiler room, coyote flips over on it's back, kicks it's feet a few times and then expires.
I've used Winchesters 45 gr HP load on coyotes, everyone I shot with that load I had to shoot twice to keep them down. However in all fairness I've never shot a coyote closer then 200 yards with that load and most of the shots were with an AR.
When it comes to my 22-250, I like the Sierra 55 gr Blitzking bullet #1455.
With the shot placed right they drop like a rock.