If I understand it correctly, aquarium fish produce NH3 as their waste product and CO2 due to respiration. Producing NH3 increases water pH due to its equilibrium with NH4+. Producing CO2 decreases pH due to its equilibrium with H2CO3 and its equilibrium with HCO3-. My question is: Which of these effects is more important in most common aquarium fish? Do fish increase or decrease water pH?
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.