RE: This may be a dumb question...
A lot of taxidermist around here won't skin a coyote- because they can make easier money on deer and not waste their time with stinky old K-9's. If you find a taxidermist willing to do it, it won't take him long but he'll probably charge you $10-20 for his effort.
As for tanning, unless you flesh it- it'll costs you $40-60 in most cases. You can send a fleshed pelt toMoyle and get it back for $23 but they charge a 100% fleshing fee... which means $46 total if you just sent it green.