I have Pyrs and love them. They have been bred for generations as LGD dogs but not all Pyrs are great LGD's. Other breeds are the same way, Anitolians, Kuzavs, etc.
I recently went to a seminar and one of the speakers was a PhD who has studied and worked with LGD's since the 1960's. After a very long and rambling presentation, he boiled it down to this: Most dogs will be great as LGD's as long as they are exposed to and live with the animals they are supposed to protect from a very young age, about 3 weeks.
I think the primary source of deterent for a predator with a LGD is intimidation. Predators just don't want to risk an attempt. So I would suggest a medium to large breed with a big bark (Pys fit this decription exactly). Get one from someone who raised it from puppyhood with the animals, or adopt a very young one. I personaly don't like the idea of a puppy being away from mommy at 3 weeks and bottle feeding is a chore so I recomend the former.