There are warm season grasses and cool season grasses. Warm season grasses germinate in the spring and, since they are heat and drought tolerant, are generally green throughout the spring and summer. They begin turning brown in the fall and remain so throughout the winter. Cool season grasses germinate in the fall and are green and growing throughout the winter and spring, but die back in the heat of summer. Although there are native cool season grasses [e.g., Poa arachnifera (Texas bluegrass), Elymus canadensis (Canada wild rye)and Nassella tenuissima (Mexican feathergrass)] that will tolerate some shade, it is actually a little late to plant them. They should have been planted in the fall to insure good germination and should be growing already. Even the non-native rye grasses (Lolium spp.)—cool season grasses ready to germinate and grow rapidly through the fall and winter—are not likely to germinate well and grow enough to help with your bare lawn. Additionally, we do NOT recommend the non-native rye grasses—Lolium perenne (perennial rye grass) or Lolium perenne ssp. multiflorum (annual rye grass)—for the following reasons:
Rather than trying to seed a grass or other ground cover at this particular time of the year, you would be better off planting small nursery plants. Sedges, which are very grass-like, would be ideal for your shady backyard. The ones listed below are evergreen, generally do well in the shade and don't grow very tall—and, thus, require little if any mowing.
Carex texensis (Texas sedge) grows in sun or part shade.
Carex perdentata (Meadow sedge) prefers the sun, but will grow in part shade.
Carex cherokeensis (Cherokee sedge) prefers part shade. The leaves of this one are a bit coarser and the plant is taller than the other two, but it is still an attractive plant.
You should be able to find some of these as small plants in local nurseries that specialize in native plants. (See our National Suppliers Directory to search for nurseries.) I happened to be in one such nursery, Barton Springs Nursery, in Austin just today and they did have small containers of Poa arachnifera, Nassella tenuissima (synonym = Stipa tenuissima), Carex texensis and Carex cherokeensis. There are, no doubt, other nurseries in the area with these species for sale. With the ground soft from the recent rain, it should be relatively easy to plant these. Usually the plants in the containers can be divided in order to cover a larger area.