Dig up a coral vine sprout with a trowel, carefully removing all the roots. Alternatively, cut off a coral vine branch with a pair of garden clippers near the soil line and dig up the tuber it was attached to, which should be just under the soil. You may have to divide the tuber away from other tubers with your trowel or a knife, but that's OK.
Replant the transplanted sprout or tuber to the same depth as it was planted before. Coral vines tolerate most soil types, but perform best in well-draining soil. Choose a sunny location with at least four hours of sunlight a day, but it will bloom best in areas that get at least six hours of sunlight a day.
Water the area well with 1/2 inch of water. If it is fall, cover the planting site in U.S. Department of Agriculture zone 8 with 2 to 3 inches of mulch, such as shredded leaves, to protect the transplanted roots for the winter.