If the coyotes are at longer ranges out to 150 yards, I would suggest a 17 HMR. It will kill them but about half of the well hit coyotes will be able to run off and die somewhere else. In my experience the 17 HMR is lethal on coyotes but is underpowered for reliable on the spot kills. With the 17 HMR, the noise level is a minimum and once the tiny 17 gr bullet hits the ground it disintegrate and minimizes the possibility of ricochets.
If you want to drop the coyotes in their tracks, then a 223 Rem or 243 Win caliber would be my choice. I would suggest the 55 gr bullet in the 223 Rem and the 80 gr bullet in the 243 Win calibers. Each pack plenty of energy to reliably drop a coyote. At the longer ranges, you will need a scope sight on any rifle you choose. I would suggest a 3-9X scope. I would leave the scope on 3X power and then for a long distance standing shot, if you have time, switch to the 9X power.
The Remington Model 7 in 223 Rem or 243 Win caliber would be a good choice.
You might want to consider calling the coyotes into range for shooting. On my Coyote Hunting Page I have a number of coyote calling sounds, Hurt Rabbit or Chicken in Distress, for example, that are free downloads. One can burn them to a CD and use a Boom-Box for calling or something similar. Calling them has the advantage that the coyotes will come to the sound expecting a free dinner when you are ready for them. To help in accurate shooting you can make a pair of Bi-Fur-Pod shooting stick for a rest in the field.
Good Hunting... from Varmint Al