I found a Rosie O. Blanton (b. SC)in the household of Elisha and Georgia F. Blanton in the 1920 and 1930 Censuses of Horry County, South Carolina. It shows her born about Jul or Aug 1919, if the information was given correctly.
It seems likely that she was born in Horry, since the family was there for both censuses. However, it is possible that she could have been born in a hospital (or home) in an adjacent county. However, there was only one Elisha Blanton in the SC census both years.
For this, you should be able to order a birth certificate from the Dept. of Health:
http://www.scdhec.gov/administration/vr/I would add a note that there was only one Elisha in SC and that you are not sure of the county.
If your mother was married before 1950, you would have to write the County. Here are some addresses for Horry Vital Records:
http://www.rootsweb.ancestry.com/~schorry/reference/vital_re...Bob Stafford