Don't have a specific gun just for coyote, but if I wanted to hunt/call 'em I guess I'd use
my Rem.700 LSS Mtn.rifle in 270Win. with Rem.100gr. ammo.
If I were to want a cartridge just for varmints, including coyotes, it would be the 243Win., with a 3-9x scope. Not sure of the rifle - lots of good choices available.
Oh yeah, ammo would be Federal Premium 85gr.HPBT.
I used a 243Win. when I lived out west, and it worked great for rockchucks, coyotes,
jackrabbits, etc.
Was passable on antelope too.