I don't think there is anything you can use that would allow for drainage and that your dogs won't track all over the house after it rains in the box. Do you know if you dog's would even use this new area after a good rain? Have you tried any lawn care suppliments or seeding in grass that is resistent to dog damage? Try your local lawn care store or hardware store. Also, what do you feed your dogs, it is possible that a reduced protein diet would help keep you lawn greener. I just use a sprinkler on the dog area of the yard to dilute the urine on the grass. http://www.yellowgrass.com/ Some people swear by the stuff on this website while others opt to treat the lawn not the dog.