Atkins use to believe that consuming aspartame was conterproductive in weight loss. The thought was that it knocked some people out of ketosis, which is the fat burning stage when doing atkins or CKD. I lost 20 pounds and drank tons of diet soda and water. Maybe I could have lost 30, who knows....
My theory if you are doig CKD or atkins, drink some diet soda, then test yourself. If you are not doing a ketogenic diet and if drinking a diet coke will help, then go for it.
Also the diet board generally recommends diet dr. pepper. THe reason is because it does not have the citric acid(pretty sure, that's it) which may also knock you out of ketosis.
Hope this helps! Good luck.