Is there a ground cover that can be used instead of grass in Arkansas

Mondo grass. Doesn't even have to be mowed.

UofA Cooperative Extension Service:

https://www.uaex.edu/yard-garden/resource-library/plant-database/ground-cover/groundcover-common.aspx

I would not use grass.instead, outline with your choice,inside put mulch, decorative rock,whatever you like and don't leave flat.build it up and set statuary 's or potted plants .i think it would be more interesting on corner to look at.hope this gets your mind churning.

Creeping thyme and sedum are my 2 all time favorites!

I saw where creeping jenny was recommended for Arkansas but there was only a picture - no article so I'm including a generic article here:

https://www.gardeningknowhow.com/ornamental/groundcover/creeping-jenny/creeping-jenny-ground-cover.htm

Good luck!

Lillies of the valley are low growing and spread easy. You'll have little white flowers most of the summer. Monkey grass also is low growing about 12 " has little purple flowers. I would edge this area with some kind of wood or stone border, as pretty as they are they spread if not controlled

love the creeping sedums too. The fall sedum gets about two feet tall and comes back every year as do the monkey grass and lilies. You can plant petunias they love the sun and will spread. They bloom all summer but have to planted every spring

The challenge is not only how much light the area is getting. The large pine trees most likely have some significant roots that are sucking both water and nutrition from the area. If you choose any of the above suggestions of living plant ground cover you may need to raise the area with some good soil mix (if there are no exposed roots on the trees) and put in a temporary sprinkler system or drip irrigation in order to establish the new plants. Some of the suggestions offered will be better suited for dryer situation than others. Be sure to do some good research on the ones that appeal to you before planting. A lot of the ground cover plants will come with very small rooted sizes. The smaller the root mass the more often you will need to water in order to keep them from drying out in between watering. Once they are fully rooted in you can decrease the water unless you hit a drought period.

There are some turf grasses that can be established that require less sunlight and can thrive (once established) through drought conditions. Check out Bermuda 'Celebration' . My map shows it as growing in Arkansas. I sell it here in Georgia.

Here is their main web information site. http://celebrationbermudagrass.com/