Yes, some swans will keep the geese off your property. No, they do not eat their own feces, and yes, just by their inherent size, they can also defecate in large amounts. However, you will only have two swans as opposed to 10+ geese pooping on your lawn. You might try using some predator markers, i.e., get a cardboard or plastic replica of a fox, coyote, etc. Make sure that you place the replica(s) in different areas so that they do not appear to be stationary. Make sure that they can be wind blown so they look like they are moving.

Another idea. Do you have a dog or does your neighbor have a dog? DO NOT let the dog off the leash, but allow the dog to walk and bark as soon as the geese land. You may need to keep the dog in the area for several hours and a couple of days. Once the geese get the idea that there is a predator in the area, they may not want to come back to your yard. The Regal Swan