The most common base cola recipe available is the "Open Cola" project.
OpenCola (drink) - Wikipedia, the free encyclopedia
The ingredients are not terribly easy to come by, but you can find them all online.
Here's a FANTASTIC episode of "This American Life" that discusses the production of cola. Listen you wont me dissappointed.
Original Recipe | This American Life
I would suggest buying a pre mixed cola flavoring, then add in your own diet sweetener.
Sweeteners will be the hard part of making a diet cola...
: 200x sweeter than sugar minimal aftertaste. aka, Equal, Nutrasweet, Canderel. Looses sweetness if heated
: First artificial sweetener. 50x sweeter than sugar. Illegal in the USA.
: 30x sweeter than sugar. Metallic Aftertaste. Illegal in Canada.
: 600x sweeter than sugar. Minimal aftertaste. Aka, Splenda.
: 200x Sweeter than sugar. Aka, Sunett.
Because sucralose has 83% of the calories of sugar, by weight, and you'll have to use SO LITTLE it's exactly what I would suggest. Though nothing will ever beat real sugar.