There was a guy in my hometown who had a greyhound that loved to run for coyote. Run straight out, slam the coyote before it knew what was happening. Then turn tail and run back to his person for cover, as it did not want to actually fight the coyote.
Basic guideline you need a team, fast enough to catch but tough enough to fight.
I have no experience doing it though I've read those who have.
It doesnt work well usually, I've only had a couple of dogs that coyotes didnt tear ass away from or scare away. Foxhounds work well, as do most of your larger terriers, id also imagine an irish wolfhound would be perfect for the task. Suprisingly I have a Lab/Chesapeake Bay Retriever mix that loves to coyote hunt.