How can I make a separate area from my lawn

A fence for your pups will be the first thing so they don't continue doing their business elsewhere. If you give them a large enough area they will be happy and you will have a nice lawn elsewhere.

I have the same issue as I board dogs, so I have to have a huge fenced yard. I made different areas of bark chips, white pebbles, flower pots and yoga mats. They treat each area differently. Walk/ run on bark, pebbles, lay on mats, and go behind 12 feet of assorted potted plants to do their business. It didnt cost a dime, just reorganizing the space from a dogs view!!