Malpighia glabra (Acerola) is a truly beautiful flowering shrub, and we wish you could grow it in Conway AR, too. Located in Faulkner Co., when we look at the USDA Plant Hardiness Zone, it appears you are in Zone 7a. Austin is in Zone 7b.
From our webpage on this shrub:
Water Use: Medium
Light Requirement: Part Shade
Soil Moisture: Dry
Soil Description: Sandy, Sandy Loam, Medium Loam, Clay Loam, Clay, Limestone. Well-drained.
Conditions Comments: Half of the winters in the Austin area are mild enough for Barbados cherry to keep its leaves. It is useful as a dense screening hedge that may be left soft, sheared, or as a specimen. Birds quickly gobble up its bright, edible fruit and adult butterflies feed on the nectar. Standard tall and dwarf spreading varieties exist."
If that sunny sheltered corner we suggested is too much sun for the plant in the summer, that blows that theory. This is really your decision to make. If you feel your soils match what is needed by the Acerola and that it can get through your winters, it's certainly worth a try.