Take rifle, shoot coyote, call rifle coyote rifle. Pretty much it.
Range for your hunting? 150-250 yards? a .223, 222, .224,22-250, 243, 6mm. Hell, toss in a 30-30, 25-30, 308, 257, 6.5x55, 7mm-08 etc.
Seen 12ga and 16ga used, I've used .22mag, 30-30, 308, 6.5x55 I've just used whatever, nothing dedicated to long range yote hunting.
I suppose if I was going to buy a dedicated rifle, it'd be the Savage 12 FCV varmint rifle. If have the bucks, a nice Swiss Arms as it's not an AR and shoot yotes to your hearts content.