If you're want to put down sod, you might want to look into some of the newer varieties of zoysia, particularly Zeon and El Toro. These are both supposed to be quite shade tolerant and El Toro stands up to traffic well. We put down Zeon (I think) last Fall, so it's too early to tell if it's going to do well under our oak tree, but I've been assured that it will. It certainly looks beautiful so far.

Here is a link that might be useful: Zoysia varieties

I've always thought of zoysia as a sun-loving grass species....as are most turf grasses. I guess you could call it somewhat tolerant of mildly shady sites, but don't expect it to thrive under the canopy of a large shade tree.

In the deep South, promises that At. Augustine will do well under the canopy of live oaks trees run rampant. It doesn't thrive, but barely hangs on until it eventually dies. St. Augustine is more shade tolerant than zoysia.

You can probably help it to languish longer by careful cultural practices: set the mower higher than usual, water deeply but infrequently, avoid excessive fertilization (or even normal doses) to help shade grown turf grasses do better, longer.

If the bare patches coincide with the tree canopy, then you might consider a nice thick layer of mulch, rather than grass. Then you can plant some evergreen ground cover here and there. Many ground covers can really take off under such conditions!

Where are you located? We might be able to come up with some good ground cover options for you, but can't do so without know your general location.

I was wondering how your grass is growing, Mollie. I am having the same issues and am looking for a solution to what type of grass to plant in my shady (not deep shade) backyard!