South Carolina didn't start to record births until 1911 so that option is out.
In Chester County marriages weren't recorded until 1911.
1820 Chester, Chester, SC
1840 Chester, Chester, SC
1850 Chester, Chester, SC
J. B. Coulter, b. SC, 50, farmer
J. C., wife, b. SC, 50
M. J. dau, b. SC, 18
The South Carolina Archives, www.archivesindex.sc.gov/guide/CountyRecords/rg0012.htm
has the following for the time frame you're looking for:
Register of Mesne Conveyances 1785-1956
Commissioner of Location, Plat Books 1822-1857
Clerk of Court, Miscellaneous Index 1802-1860
Court of Common Please 1800-1843
Court of Equity 1820-1868
Court of Equity, Equity Bills 1821-1868, etc.
The Camden Archives and Museum, http://cityofcamden.org/departments/archives/museum
has microfilm but you'll have to contact them to see what it covers
The Chester District Genealogical Society, http://homepages.rootsweb.ancestry.com/~scroots/sc07606.htm
has various publications
Look for books about the history of the county.
Finding records in South Carolina is like finding hens teeth. Successful Searching!