What do you do with your coyotes after you polish them off? I am sure that any number of other animals would love to feast on the carcass. But I am not sure how "wanton waste" factors into coyote hunting.
One thing, if you eat 'em, please keep that to yourself
You can burn and bury them
dump them in a farmers "dead hole" which I do a lot
a lot of times i throw them in my trash and let the garbage man haul them away every tuesday
You reminded me of a story I am embarrassed to admit. Several years ago, I tried unsuccessfully to hunt the coyotes that were threatening grandma's cat and shortly thereafter accidentally hit one with the car on the highway. A passer-by showed some interest, but I don't recall what happened to it after the state trooper shot it to finish it off.
I would look online or talk to a local gun shop for a fur trader in your area. If it is not terrbily destroyed they will give a few $$ to the shooter for it. If you want to get deeper into it, you can skin and tan them yourselves and get a bigger $$ from fur buyers. That way nothing is wasted.