The following is a quote from the Georgia State Archives website:
Free Persons of Color Registers, 1790-1865: Registers usually include name, age, occupation (sometimes), property, and white sponsor. Available for 21 counties: Appling, Baldwin, Camden, Chatham, Clarke, Clay, Columbia, Elbert, Emanuel, Hancock, Jefferson, Jones, Liberty, Lincoln, Lumpkin, Pulaski, Screven, Taliferro, Thomas, Warren, and Wilkes.
The above are on microfilm at the Georgia State Archives.
A transcription of the resgister for Augusta has been publised. Go to google and use "free persons of color" to look for its location.
I have transcribed the one for Clarke County and have more records on these people from the census and tax digests and miscellaneous records. I have seen the one for Elbert County and it is a very good one--running for many years with detailed information.