Do fish increase or decrease pH of aquarium water?
Like a glass of beer going flat, any excess CO2 that your fish produce will quickly and irreversibly escape into the atmosphere. Thus, at least in terms of the pH battle between NH3 and CO2 that you describe, NH3 would win.

boilerplate "science is complicated" disclaimer

That said, it's likely that the total environmental effect that fish have on a tiny non-circulating volume of water will be much more complicated than the interaction between two basic chemicals. For example, say one of your fish sheds some scales and they start to rot. All sorts of things would be happening at that point which could affect the pH.