a Mr. Goodbar cake calls for a can of Coke Zero - would another kind work?

There are bunches of cake made with cola (or other soda). Partly for flavor, partly for carbonation.
https://www.google.ca/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=cakes+with+coca+cola
If you're worried about using artificial sugar, substitute either a plain club soda or a regular cola.

I would wonder about the sweetness level if substituting. According to chef Google Coke Zero contains Aspartame. The later is broken down by heat and looses its sweetness. So the Coke Zero is presumably contributing flavor but not a lot of sweetness.

I've never baked a cake with soda pop before, but I'm guessing the Coke Zero is just for a calorie reduction, and assume you'd be fine with another kind.