I prefer to use a bow for deer but here is what I use on deer killers...
For Coyotes- Ruger M77 Mark II .243 with Winchester Silvertip Ballistics 95 gr.
For Bears 1930's Mauser small ring 98 8MM with self loaded ballistic tips 170 gr.

This was brought back from Germany by my grandfather during WWII. All gunsmithing and stock fabrication was done by a German gunsmith.