I bought a very large tote, the biggest one they have at Home Depot. When i get one, i put fresh dirt in the bottom of the tote to soak up blood.
At either the end of the day or in the middle of the day when calling gets really slow, i will skin the mornings coyotes.
I spray Flee and tick spray on my sleeves, and gloves. Then skin, and roll up with fur side out, so the face is on the outside. (handy when it comes to fleshing later)
I then put the hides in a trash compactor trash bag (thicker bags) and then spray the spray into the bag and tie it closed. When i get home they go in the freezer and wait until I flesh them and put them up.
Doing it this way has kept them off me, and killed them in the bag while in the freezer.
Good luck
For skinning, i got some square 1-3/4" pipe that is .120 wall and built this skinning rack that goes in the tow hitch. It works great since we usually don't have a lot of tree's here, and it's also helpful for loading Elk. I use a comealong to lift the chest and then grab the legs and pull them into the truck and then lower the comealong. I usually hunt by myself so i had to get creative.