RLA: Seek out a "lightly used" Remington 700 in one of the many and varied "Varmint" type models.
These are on occasion found at very pleasing prices and in the aforementioned lightly used condition.
I have right at one dozen (12) of these type Rifles (many of which were bought used) and they all are very accurate+!
Afix a Harris swiveling bi-pod to the Rifle and get after those Coyotes big time!
Best of luck to you, and by the way I have had very good luck on a couple of Rifles with the plain old Remington 55 PSP ammunition - both accuracy and lethality on all manner of Varmints (and DEER!) has been pleasing.
Hold into the wind
VarmintGuy