Much good advice above here, especially: 1) setting pan tension to a) avoid non-target animals and b) to allow a coyote to fully commit to stepping on the pan before it falls,2) bedding the trap solidly, and placing it in proper relationship to the dirt hole.
I will say one thing further, if you are sure the hair you found was coyote hair, I agree it may have been that someone shot your trapped coyote and then stole it. Once, I had a guy "help" me by shooting a coyote I had trapped with a 270 deer riffle, at near point-blank range. There was a lot of blood!
