Tim Gallwey's approach to coaching resonates strongly with me. The "Inner Game of Tennis".
He's the only documented coach I've seen who teaches the student how to properly view their own learning. Dealing with the mental side. Also, though he taught fundamentals, he also allowed the student's natural physical/mental tendencies to develop into a game suited to that student. I think this is powerful.
Also, the approach of the coach not saying a whole lot. I like that, too.