This is a very good question for the Atlanta Fruits yahoo group, because it is my understanding that NO apricot does well. Apricots are in the almond family, and most almond family plants do not like humidity, to my understanding.
If you were to grow an apricot, I would imagine a very regimented spray program would be necessary for any sort of success. However, the Fruit group could help out.

Thank a bunch, Girlgroupgirl, for the information. My apricot is dying either from late frosts or some kind of disease. As far as Apricot Variaties, Late blooming type might work for Atlanta area. Oak Creek Nursery has listed the apricots for late frost areas.

Here is a link that might be useful: THE APRICOTS FOR LATE FROST AREAS