That dog weighs more than me. Anyhow, consider a groundcover such as liriope or creeping phlox. They should stand up to dogs, and may require less water and maintenance than a lawn.
We have two very Very large big boys! We use pee gravel in thier kennel habitat, it works wonders during the rain here in the pacific NW
Those are a couple of very handsome dogs, Debbie, but if they have free run of your lawn area, I don't held out much hope of even a ground cover surviving. In addition to the ones Steve mentioned, you could try blue star creeper (Isotoma fluviatillis), but for any of them it is crucial you keep the dogs off until the plants are very well established. Good luck!
Debbie, I have seen a few companies offering a good looking artificial pet turf that is pet urine resistant. It takes some work for installation (a base material etc) but you can get some "grass" look that they claim stands up. And of course, low maintenance. Here is just one website (but there are others): http://www.easyturf.com/pet-grass-dog-grass I don't have any personal experience to report on which may be better than others but it may be "cheaper" in the long run than fighting a losing battle with dogs in the yard. I always worry about pea gravel because I have seen a lot of it passing through a dog (it is used in some areas at Canine Assistants) but bigger stones have gotten lodged in a dog's intestine. Surgery can be done if that happens but we have unfortunately, as with any surgery there is risk and sometimes very sadly the worse happens.
I like Kevin's advice. There are no grasses (or other plants either) that would withstand in Georgia the constant tramping of a 150 pound animal.
We have found that the only thing that holds up to dogs is Artificial Turf. We have used it on many back yards for dog areas and all of our customers swear by it. It is a 5-6 year investment compared to sod but well worth it. You will always have beautiful green lawn that the dogs can run freely on with no damage or dirt tracking back into the house. Here is the link to the turf we use the most. They can even help you out with a contractor to install it if you need one. www.ecowaterlessgrass.com
My two dogs 87 & 103 lbs have had artificial turf in their 30' dog run/potty for about 8 years. It still looks great and we only use baking soda and water to clean it (after some manual pickup). I believe we have 5" of small stone and some sand underneath the turf.
Today they make even better artificial turf.
One of our local dog park gave up on the grass and put in mulch. We took the idea home with us (lined with edging), and it has been great-- but I did read up on dogs' chewing and a good type of mulch to buy (which hasn't been a problem for us, it turns out, but all dogs are different). Good luck!
I have now had the dog run with artificial turf for over 10 years as a dog run/potty. Since I saw another type of artificial turf that is made for a dog potty I've decided to replace the one they have. We'll see if the newer technology is better. We will be installing it next week. Mulch would not work in this dog area as it would be way too difficult to clean up.
I moved from a home on nearly 5 acres to a small cottage-neighborhood in the Pacific Northwest. No drought issues here, but because I have Great Danes...and only a smallish yard for them, keeping their potty area clean and pretty became a real issue. I tried planting a lawn for them, but with big dogs...in a small area...it couldn't get established. I tried REAL lawn turf...that was a disaster, and expensive when it turned pee-stained and ugly, quickly. So, I checked into artificial "Pet Turf"...there are MANY different products all with different names...I ended up with "Dream Turf" out of Seattle but installed by a company in OR called Cascade Greens) loved the idea...and paid to have it installed professionally. I've had it now, for 8 years...and it is the BEST thing I could have possibly done! My big gang lives INSIDE the home...and uses the PET TURF area pretty much just for lying around when it's sunny out...and for going potty. Underneath the turf the yard has had all the grass and several inches of soil removed, and if necessary drainage work is performed. The soil which WAS there is replaced by a deep layer of aggregate material...which is graded, contoured and shaped (sounds complicated but it's really just "raking") ...and then it's covered by landscape fabric to prevent ALL weed growth.The turf is laid out to allow for as FEW seams as possible...and then those seams are glued with a special glue. The whole thing is anchored with special spikes...or nails which go deep into the aggregate. Then a special "antibacterial filler" (which is a fairly new product...replacing the old rubber sand that was previously used.) This new stuff, in the form of almost invisible tiny green beads...weighs a TON and is so WORTH it, because it keeps the bacteria and thus odor from forming and thus no flies are attracted as long as you faithfully hose it down, at least once a week if you have a lot of dogs, as I do. The backing of the turf is already MADE so the urine flushes through into the layers of aggregate... and the beads are added to the surface of the turf...and worked deep, down into it, for stability and again, for bacteria/odor control. I handle the feces by scooping...and flushing it right down our toilet. Because my area is so small...I also hose down after every poop. (Most people have fewer dogs...and a larger area so don't feel the need to DO that; but in my case this method works best for me. If you have a husband...(which I don't) he could do the majority (if not ALL) of the work required for such a project. The other super thing about this turf...is it lasts for years and years, and except for a quick 30-60 second "hose job" there is NO prolonged watering...and no waste...virtually no maintenance...and the yard looks just fabulous, all year round, even in places with 4 seasons! (Think about it; NO MUDDY PAWS!! EVER!! In drought plagued areas of the country...pet turf is going to become almost the norm, I think...as many cities and states will no longer ALLOW lawn-watering. I really do LOVE my turf...and would recommend it to anyone. There are reputable turf companies all over the country...and the products have greatly improved over the last few years. Do your homework...and look into it. I don't think you'll be disappointed.