You could get a .223 Rem., heavy barreled Savage. Send it to Fred Moreo of Sharp Shooters Supply, have him ream out the chamber for the .22-243 Ackley Improved, replace the bolt head and your in business with a very long ranged varmint rifle. A friend did just that and the 1 in 9 twist stablizes the 69 to 75 grain bullets well, with muzzle velocities (depending on the bullet) in excess of 3500 fps.
However, a lot of guys around here who hunt coyotes with dogs have preferred a 6 X .284 for shooting the shots at coyotes out in the middle of a corn field.