I have lived in the South pretty much all of my life. Nobody calls all soda 'coke' as a blanket term in any part of Georgia, South Carolina, North Carolina, or Tennessee I've been to. Maybe some backwater regions do, but where I have experienced dialogue, 'soda' is the general term. Now, I usually order a Coke at a restaurant just assuming they have it, as Pepsi is much less common here (also I despise Pepsi), so maybe that's where this misconception comes from. That's my theory, anyway.
And yes, I have spent a fair amount of time in Atlanta. Even there, the idea of calling a beverage 'Sprite coke' is completely alien to me. There are cherry cokes, grape cokes, etc, but that's because those flavors of Coke actually do exist.
Now, if you want to hear weird, I will admit that I have heard many elderly people call Coke 'co-cola.' It might just be an antiquated colloquialism for coke that's gone out of style.
I lived in various parts of NC from 1968 to 1987. When I first arrived, the standard greeting when visiting friends was "Can I get you a coke?". If the answer was affirmative, the followup question was "OK, what would you like?" and you were then expected to name the beverage you preferred. Interestingly, the answer in many cases was "iced tea", but the generic term "coke" was meant to cover all non-alcoholic beverages, carbonated or otherwise.
This usage seemed to be more prevalent in the more rural areas, particularly in the eastern sections of the state. In more urban areas (Raleigh, Greensboro, Winston-Salem, Charlotte), it was less widespread in my experience. By the time I got to Chapel Hill in 1977, I had either become so used to it that it didn't register, or it didn't happen as much there (perhaps because we were mostly drinking beer). When I go back now to see family, I don't hear it very often.
Both my maternal grandparents referred to Coke as co-cola, as if the extra syllable on the bottle was one too many. My grandfather would only drink his Coke from the small 8 ounce bottles, and as a youngster I can remember being assigned the task of keeping up with the bottles (for the deposit) on the runs to the grocery store. Pepsi products were never served in that household, which is odd, given that Pepsi was invented in New Bern (by a Chapel Hill grad).
