I was in a golf scramble a few weeks ago where my company hired a photographer to get action shots and pictures of all the teams. His approach seemed to work really well for him. He found a green and tee box that were very close to each other. He used a 5Dm2 and 70-200mm f/2.8L IS II USM. He would get pictures of our approach shots (~70-50 yards away, he had an extender, but he said he only brought it "just in case"), and then shots when we were putting on the green. Before we teed off on the next hole (again, tee box was right next to the green), he would ask us to get together for a group shot. Then he would -- with our permission -- get shots of us teeing off.
So he got a wide range of photos -- approach shots with short irons, putting, teeing off, and a couple of groups shots. He did this on holes #2 and #3, and when all the teams were finished with those holes, he got in a cart the course let him borrow and drove around taking pictures for another hour.
His approach (no pun intended) worked really well, and he really didn't have to put in a ton of effort trying to get nice pictures. And even more important, he didn't annoy the golfers while going about his photog duties.
Even if you're not the primary photog at the course, the green/tee box approach would work very well.
Hope this helps!
