Cocktail attire would mean, well, a cocktail dress. Not formal, but not casual or business. It would be street length or tea length and fairly dressing.

In most areas of the country a black cocktail dress would be perfect, but the South tends to be more conservative and in some areas wearing black to a wedding is still a symbol of disapproval of the marriage. Perhaps someone who lives in SC can give you an idea of the appropriateness of a black dress. Do stay away from a long dress.

Some kind of evening fancy dress, not long. A chiffon or silky (spaghetti strap, sleevless, strapless, fancy sleeved) dress with or without beading or a few sequins. Evening shoes and little evening purse. Bring a scarf or pashmina shawl if it is outdoors.

I think the idea is a short dress or skirt or a pants outfit, with evening fabrics, shoes, and accessories. I'd wear a party dress or good slacks and a dressy top with "party" shoes and evening accessories. They want you looking like you're dressed to celebrate, not for the office.
If you already have something perfect that is black, I think you will be fine if you have plenty of festive color and detail in your outfit -- scarf, jewelry, jacket, accessories -- i.e., that it's clearly a party outfit, not something you could wear in the daytime to a funeral! I know the symbolism of black at weddings holds in some places, but I bet you'd fit in better with a sharp little black party dress than with, say, a severe navy blue or gray business suit.

i'm from georgia and most people i know (uner the age of fifty) think that it is perfectly acceptable to wear black to a wedding. I think that a little black dress would be perfect for the wedding (but you could ask someone just to be sure). you should dress it up a bit though, with a bright scarf or jacket.