Hornady 52gr BTHP or Sierra Varminter 60 grain hollowpoint are the most fur friendly yet lethal bullets I've had experience with out of the .223.

Nosler 55gr. E-Tip is a pretty good bullet too but I've experienced more runners with those. But can't remember ever losing any because they didn't run far.
I didn't climb to the top of the food chain to eat carrots.