Ask Mr. Smarty Plants

Since you did not specify the sun exposure on your slope, nor say how steep it is, we can only give you a general answer, based on a previous answer which involved the same general climate and USDA Hardiness Zone of 8a. We also cannot guarantee that the area will stay green all year. With careful choices of which plants, the area will, at the very least, stay attractive all year. 

Grasses and sedges are excellent choices for erosion control.  Their extensive fibrous roots will help to hold the sandy soil in place. You will need to read the "Growing Conditions" for each species recommended below to see if their requirements for light, moisture and soil type match the conditions at your site.  Here are some suggestions for grasses native to your area:

Andropogon gerardii (big bluestem) 4 to 8 feet tall and grows in sun (6 hours or more of sun per day) or part shade (2 to 6 hours of sun per day).

Bouteloua curtipendula (sideoats grama) 2 to 3 feet and grows in sun or part shade.

Bouteloua dactyloides (buffalograss) 3 to 12 inches and does very well in sun but not very well in part shade or shade (less than 2 hours sun per day).

Bouteloua gracilis (blue grama) 12-14 inches and, like buffalograss, prefers full sun.

Chasmanthium latifolium (Inland sea oats) 2 to 4 feet and grows in part shade or shade.

Muhlenbergia reverchonii (seep muhly) 2 to 3.5 feet and grows best in sun.

Panicum virgatum (switchgrass) 3 to 6 feet and grows in sun or part shade.

Poa arachnifera (Texas bluegrass) 1 to 1.5 feet and grows in sun or part shade.

Schizachyrium scoparium (little bluestem) 1.5 to 3 feet and grows in sun or part shade.

Sorghastrum nutans (Indiangrass) 3 to 8 feet and grows in sun, part shade or shade.

Tripsacum dactyloides (eastern gamagrass) 2 to 3 feet but can reach 10 feet and grows best in part shade.

Carex blanda (eastern woodland sedge) grows to 12 inches and in sun, part shade, or shade.

Carex cherokeensis (Cherokee sedge) 12 to 18 inches and grows in part shade.

Carex planostachys (cedar sedge) grows to 12 inches and grows in part shade.

Carex texensis (Texas sedge) 10 to 12 inches and grows in sun and part shade.

Although you are not creating a meadow or a lawn, "Meadow Gardening" and "Native Lawns" in our HOW TO ARTICLES have useful hints for planting and maintaining native grasses.  You can also include some wildflowers with your grass species in your planting but the grasses should be predominant for the best erosion control.  You can see a variety of wildflowers for your area in our Recommended Species list, click on Louisiana on the map, indicating herbs (herbaceous blooming plants), annual, sunlight available; you can check our National Suppliers Directory for seed companies and nurseries that specialize in native plants near you.

I don't know how large an area you need to cover.  If it is small you might be able to use grass plugs.  However, if it is a large area, seeds may be a better solution.  Since you indicate that the slope is steep you might consider using an erosion control blanket.  The erosion-control fabric works by slowing the 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 also 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.  Many nurseries carry this erosion control fabric. 

Here are a few selected photos from our Image Gallery of the grasses and sedges listed above:

Andropogon gerardii

Bouteloua dactyloides

Panicum virgatum

Schizachyrium scoparium

Carex blanda

Carex cherokeensis