If there is trapper nearby he'll probably pay something for a pelt taken off properly, a bit less if it's still on the carcass, but that saves you work and disposing of the carcass. At worst, he'll give you nothing for it but maybe will be a pal and give you useful info about game in the area and friendly landowners. There's at least one Hutterite colony around here that used to pay a bit for whole dead coyotes to process and sell the pelts, so if you have any of those around it might be worth checking to see if they do, too. Otherwise, as Gunslingr said, the natural process.