I doubt grass would work with so little sun. And yes you could water it alot but you will have to keep the dogs off it for at least many weeks. There have to be other options for you: vinca, ajuga, ivy, pachysandra plus many herbacious perennials.

I defined paths in my shaded garden and try to keep them mulched with chopped leaves or some other organic mulch. My dog appreciates this because he thinks I spread the mulch just for him and he does his thing in it. Then his souvenirs are easily spotted and picked up. Under the trees I've raised the beds slightly, just enough so that it still looks fairly natural (not much of a deterrent to large dogs, I realize, but mine is short), and I've filled the beds with hellebores, ferns, and epimedium. When I'm trying to establish one of these plants I protect it with a small-sized peony frame. This keeps my dog from running rough-shod right over the top of the plant, and holds him at a slight distance when he wants to pee on it. Eventually the plant fills in the frame and grows through and out of it and by this time Doggy has another route carved into his brain that takes him around the plant. This has worked pretty well for me -- everything I've planted has survived.

wantonamara: Ours remains about 6 to 8 inches tall in our blackland prairie clay where it is irrigated when the adjacent St. Augustine is watered as needed. The blooms stop during the heat of Summer, but stays green year-round. Good to know it would likely go dormant without the extra water it is catching from the lawn. No volunteers so far in this environment. Omar: Suspected lifespan/vigor was keeping it off the recommended ground cover lists. Otherwise it seems like a great candidate for my area. Except for some thinning around the woody base during the summer heat, our 3-year-old plant remains at least as dense as in the photo throughout the year. It stays green down to at least 15ð F and is supposed to be root hardy to 0ð F - which means it would be evergreen here through most winters and survive all. However, wouldn't want to have to patch or replant such a large space every three to five years. Thanks for the help on this. Will take some cuttings and experiment in other locations, but will go with one (or both) of the alternatives for the front.

Since it’s a rental I’d get some potted plants that you can take with you. Not sure you can do anything about the ground cover however without permission from the owner.