hmmm. Watering is the only thing I know of. I think there's stuff on the market that supposedly neutralizes their pee--but I don't think I'd use anything that wasn't natural. We have 3 dogs, so I know what you mean
Our solution is a work in progress, we're getting rid of the lawn. Eventually it'll all be walkable groundcover. Hopefully one more tolerant of doggy pee. If you do find a solution, please post!