It's been 25 years since I went coyote hunting, and we came up empty-handed. Daytime hunting requires a lot of patience and bait. Use a high-powered rifle, camo, and get 250 yards or more upwind of the bait.
For night-time, a 12ga with #4 lead shot is the ticket, turkey loads. IIRC, the coyote call is supposed to sound like a wounded rabbit, but ... first time we used one we had a few brews before setting up (put out some jackrabbits we shot the day before) and when my buddy blew on that coyote call, we all busted up laughing. We got quiet again for 30 minutes, and he blew it again. This time we held back as long as we could, then laughed twice as long and twice as loud. This process repeated itself until 4 am when we finally gave up.
All the real useful advice I could offer is to make sure of your target. If it has a collar, it probably isn't a coyote. If your scope cannot discern the really tall ears of a coyote from somebodies German Shepard that apparently was allowed to run free for miles, you need a better scope.