My dogs have a designated poo area. It's just dirt covered with straw, which for some reason they love to relieve themselves on. First time I put some straw I wanted to get rid of on a pathway to keep the dust down, all my dogs ran out and started peeing and pooping on it. I'd never seen anything like it.
I take them out first thing and the little ones are on leash until they produce. First they pee, and then they poop and they each get off the leash as they start going.
They've learned that in order to get off lead to run around the yard they must "produce." The big dogs are under voice control until they do likewise, BTW. (Five dogs on leash is more than I can manage first thing in my day.) So everyone is pretty motivated to get the job done, so to speak.
Now... I feed my dogs one meal a day and one snack, and they get raw food and cooked veggie glop that creates small stools once a day. So... it may be a little more difficult for you. But if you won't want your lawn destroyed or to get into a whole deal tearing things up and trying to patch your lawn with astro-turf (or replace it, which BTW is expensive), then I'd suggest you look at some way to have them do their duty somewhere else and/or under supervision. An ex-pen or a leash or a dog run.... whatever.
If you really want to do astro-turf, I guess you do. I do know it's hot and they have had trouble on soccer fields and similar places with shoes melting. So in a hot summer climate I would not want to use it with dogs. But you'll do your own research on that.