RE: Coyote
Man, you just never can tell what will happen. If the deer are close to coming out when you shoot a 'yote, they may wait until after dark. Or it may interrupt their pattern for a day or two. On the other hand, they could come out a few minutes after you shoot. There are so many variables and unknown factors that it's kinda hard to say.
BUT - if they coyotes need thinning, and you get a good shot, you might be doing a real good thing for the herd for years to come.
I think I might be inclined to shoot one if I got the chance. If it's hanging around the immediate area of your setup, the deer might shy away anyway, and you won't see them that day. If I shot one say, 30 minutes before dark, I'd leave it lay until after dark - don't come down before that and maybe spook off some nearby deer.