Carcasses, as Joe describes, can often be worked very productively with trail sets and if possible drags.
The exact methods which work best depend largely on the surrounding terrain and vegetation. Two extremes might be sparse too heavy woods and wide open places. In wooded / brushy areas think drags and you just go round picking catches out of the trees and trap locations don't change. In this type location I have had carcasses draw for weeks and have taken 17 coyotes off of a single carcass. It seems that the coyotes stay "on guard" when approaching tight carcasses, trails develop rapidly or are there to begin with and blind sets work best as the first ring of traps from 50 to 150 yards out. A second ring of traps out hundreds of yards along main approaches can be lured with gland, urine and curiosity lures.
The other extreme might be wide open flat desert; you have little choice and must stake. Stay back with your first ring of traps and try scent posts and gland sets along trails. After you have taken a few you may find that the remaining animals get fussy, ignoring lured sets. Frequently, you will now have well established trails where you can sneak in blind sets. The final (later in the life of the carcass, so to speak) line of traps may be very close blinds just back to where you're legal and don't catch birds. I have not been able to get as big of a yield off of open country carcasses as those in tighter cover...coyotes spoke more quickly and birds clean things faster.
In both cases, but more so with open areas, I have had luck with dirt holes and bait. Both the caching and stealing nature of coyotes comes into play. I use, when ever possible, a bait taken from the carcass. A mild food lure seems to help. I use bigger holes, leave the dirt and make it look like something has already dug at the hole. I fashion this excavation into a step down sort of arrangement (in the mound of dirt in front of the hole dig a groove like a coyote has pawed at the mound, put the trap in this groove back at what ever distance works for you, maybe 10 inches from the lip and place some guide clumps along the outside of the jaw closest to the hole). These sets seem to work well along travel routes quite away back from the carcasses (hundreds of yards) and later in the time frame of things.
I use snares any place I can. However, always consider the effect of a snared critter on others coming and the effect of scavenger birds on your catch.
Joe, glad to see you can still type with all those nasty, cut, greasey, stinky fingers. :-D