Using a tape deck and a rabbit tape, I've always started out a bit loud, turning it down after the first 10 or 20 seconds. My reasoning is that it will attract coyotes from further away, and then sound more realistic. What coyote is really eager for a 400-pound rabbit?
In the dark of the moon, full nighttime seems to work better. During the full of the moon, late afternoon from, say, an hour before sundown or so works well, as does the period from first light to maybe an hour after sunup. My theory is that with a lot of moonlight, prey animals have a better chance of escape and predators have to work harder for a meal. So, they're up and moving for longer periods. Damfino; it works.
Coyotes tend to come in on a call and then at 50 to 100 yards out, circle to get downwind to smell the rabbit. To counter this, if you set up at the edge of a brush or tree line where the wind is blowing along the edge, you force the coyote to quarter in, across an open area. He can't smell you, then, and you have a more open shot.
If you use a spotlight or flashlight, don't shine it directly in the coyote's face. Catch his eyes in the edge of the beam, after you've identified him. Using some sort of red lens-cover helps. I use a Q-Beam with a red cover; works well. Even a hand-held 2-cell flashlight is okay at closer ranges, if you're not concerned about somebody's pet dog.
There are tapes of a baby goat sounding unhappy; you might use one of those, with a carcass of a coyote-killed goat out in front of you...
Good hunting!
Art