Need a Dog Friendly solution for removing grass

I have a tiny back yard and our dogs have killed the grass. I'd like to go ahead and remove the remaining turf and put down either gravel or kiddie cushion mulch only our dogs need a place to pit stop. What do you guys recommend for this occasion? I have pea gravel on my side yard and I think it might be too hot to continue it through the backyard. I really like the kiddie cushion bark mix but its hard to find. So is there a ground cover or grass I wont have to mow for dogs that can stand up to pet waste? Also, is there a tough mulch solution out there you can buy in bulk similar to kiddie cushion?