I've had success with both mouth-calls and tape recorders. In Texas, either cottontail or jackrabbit tapes have worked best. I try to imitate the wounded rabbit with my "blower".
I usually use either a .223 or .243, both bolt action. Scopes on lowest-power.
I vary with the lights for night hunting. I have a Q-Beam with a red lens cover. I use a Streamlight SL-20. Backup is a fairly narrow beam three-cell standard.
The trick with the lights is to sweep fast, just picking up the eyes. If you spot eyes, come back with the light held fairly high, so only the edge of the light makes the eyes glow. If feasible, shift to a weaker light.
I usually hunt from my truck. Sometimes, if there are others to go play with, I'll drive and call, and let the others ride in back to shoot.
Coyotes usually circle and come up from downwind, to try to smell what's happening. They trust their noses more than anything else. Staying in the vehicle helps fool them. On the ground, wind direction is a consideration when you're picking out a place to sit.
If you use a tapedeck, get one with separable speakers, and buy 100' of speaker wire and splice it in. Set just one speaker away from you (they don't need stereo), and watch from concealment...
If your country is brushy, use a shotgun. I've seen coyotes come within ten feet of the truck...Had a fox running around under it one night, barking. People kept hollering, "Shoot him, shoot him!" "Where, where?", and the fox kept running and barking...He finally got disgusted and left.
One aspect of the tape: Since coyotes are fairly quick learners, you'll find your luck tapering off. So, go to something like a baby goat tape, or the yellowhammer woodpecker tape (which will drive you nuts with its peep-peep-peep repitition.). And change locations.
During the time of the full moon, predators hunt earlier in the evening, and later in the early morning. Prey animals can spot them more easily, then. So, start in a little before sunset, maybe, or go out at first light in the morning.
Find a restaurant which will let you bring a garbage can and liner, and which will sort out meat scraps into it. (Even if they don't have time to sort, it'll still work) Set up a varmint lunch-counter, and keep an eye on it. Sweep the dirt around it, and check tracks...
Hope all this helps, and feel free to keep asking...Art