If the slope is very steep (as you have indicated), you are probably going to need to create some mechanical means to hold any plants or seeds in place until the plants can become established. One possibility is to use some sort of erosion control blanket. The erosion-control fabric works by slowing runoff water and allowing sediments to fall out rather than be washed away. Seeds are sown under the erosion-control material and grow up through the matting when they germinate. You can insert plants into the soil by cutting through the matting. The roots of the plants that are growing through the erosion-control material anchor the soil to stop the erosion. If you use erosion-control blankets made of biodegrable material, they will eventually disappear leaving the plants to control the problem. Erosion control material is available at many nurseries. There is an excellent article, Biotechnical Streambank Protection: the use of plants to stablize streambanks, from the USDA National Agroforestry Center that suggests several other methods. Now to stabilize the area, we recommend grasses for controlling erosion because of their extensive fibrous root systems that serve to hold the soil in place. You can add other perennial herbaceous and woody plants along with the grasses.
Below are some recommended plants native to North Carolina and Mecklenberg County or an adjacent county. Since I don't know the amount of sunlight available or the type of soil for the area in question, you will need to check the GROWING CONDITIONS for each of these plants to be sure that they are compatible with your site.
GRASSES AND GRASS-LIKE:
The grasses and sedges listed below are attractive. Some of them will grow best in full sun, but others will grow in shade and part shade.
Ferns generally grow in moist shade and part shade. Some of the ones listed are evergreen.
Asplenium platyneuron (Ebony spleenwort) is evergreen.
Dryopteris carthusiana (Shield fern) has sterile fronds that are evergreen.
Dryopteris cristata (Crested woodfern) has sterile fronds that are evergreen.
Polystichum acrostichoides (Christmas fern) is evergreen.
Here are photos from our Image Gallery of a few of the plants above: