Well, you want the wind blowing FROM the coyote TO you. I've always called that hunting upwind or into the wind. To me, hunting downwind means the wind is blowing from me toward the coyote (or from the coyote to me if I'm downwind of him).
If that's not too confusing.
I don't think camo is as much the deal as not having your fat little face shining if you're hunting during daylight.
It's worst in the late afternoon if you're looking toward the west, into the sun. Less of a problem if you're facing east. Night? Doesn't matter. Any sort of dull, earthtone color of clothing is just fine.
I've mostly used a mouth-blown call, imitating a cottontail or a jackrabbit. There are all manner of cassette tapes, if you use a baby boombox. (My wife says no self-respecting coyote will come toward a 400-pound rabbit. Don't blow too loud, IOW.)
A dead coyote doesn't care what killed him. There can be more gun than needed, of course, but really there's no such thing as overkill.
If you call, remember that a coyote generally will first come straight toward the sound, and then circle to get downwind for the final approach. He trusts his nose more than his eyes. So, try to set up where you can see crosswind and downwind to catch him in his circling. (And there's no such thing as "always".)
Art