I've braintanned raccoon, beaver and squirrel w/ hair on. first, you want the hide as fresh as possible. Once you get the hide, lightly salt the skin and let it dry. This helps to "set" the hair, otherwise there is a greater possibility the hair will slip during the tanning process.
After the hide is totally dry, resoak it and make sure to wash out all the salt. Then gently scrape the flesh side to get off all remaining membrane. Then, I take brains, mix with very warm water, and begin working it into the flesh side of the hide. It may take several braining cycles to make sure you get good penetration. Once that's done, either freeze it, dry it, or immediately soften it, which means pulling, stretching, and rubbing until it's totally dry. I've never done coyote, but I've seen some that have been braintanned, and they looked and felt really soft.