This is what I chose after we lost our LGD in the fire. We chose a Bernese Mountain dog because A) They don't wander (AT ALL!) and B) they are large enough to ward off potential dangers.x2. It is really important to understand these dogs, and how they work. Originally they guarded large flocks that roamed hundreds of acres, therefore, they don't take confinement very well. Two acres is a very small area for a dog whose nature is to cover hundreds, and a dog asked to confine itself to two may not be very happy. Your dog will want to roam a lot further than that - and will if you don't have fencing to contain him.
Unfortunately too many people get LGD's to guard their poultry with disastrous results. Its not that they can't be trained to leave them alone but it is not their nature to guard them. For a small property like yours, you may have been better off with a "pet" breed of dog that is poultry safe (adopted as an adult, you can assess that far more quickly than getting a puppy). Often just the presence of a dog on the property is enough to deter predators. I have two 40lb poultry safe mutts, and their dog igloo is located in the chicken yard. During the day the birds and dogs free-range and at night the birds are locked in the coop while the dogs sleep in the igloo. In the year and a half we've had this arrangement, we haven't lost a bird to a predator.
It was so easy to train my BMD to the chickens in comparison with my LGD. He had a few bouts of carrying chicks around (not one single one injured), but otherwise was completely gentle.. This is what the breed is known for. They are truly gentle giants...
I'm not saying give up on your LGD, but I sure hope someone who is considering raising one reads this and realizes it may not be the best decision for them.
I say 10 acres minimum for a Great Pyr or Maremma. They won't be happy on two.. You will constantly be struggling to keep him contained.