Not sure if your place is big enough, but I have seen this done in some local hillsides and it works great, even for brush.
Los Angeles County Fire Department - Forestry - Vegetation Management - Goat Contractors
I doubt a Coyote would take down a grown goat, at least if it is running free. I may be mistaken. The long tail big cats - that's another story.
I like goats. They make a good curry!
G