Here's one video that shows the screwdriver method of removing cartilage. Ear Cartilage removal
It will work fairly easy with fox, but you may or may not be able to pull it off with coyote. Take a close look after the ears come out and you will see that if you are not real careful you will leave parts of the outside ear attached to the cartilage. If you want a perfect job on the ears you are best using something like the end of a metal soup spoon to slowly wedge the cartilage away from the outside ear skin. Once you get to the ear edges you can cut the skin with a sharp knife. The end result will be the cartilage and inner ear fur stay on the head, while just the outside of the ear fur stays attached to the pelt.
Be patient and good luck.