A couple of ideas/suggestions. These ideas are not necessarily related, just some thoughts I've had about ways to implement the idea. I haven't taken the time to read the entire thread, so I apologize if these ideas have already been put forth.
Since the aquarium is supposed to generate income for gaia, I think that breeding would mean less people would be willing to buy fish with cash. One way to encourage more cash purchases would be to make only 1st gen fish breedable. Meaning only those fish originally purchased with cash or awarded in daily chance are breedable. They can be resold in the marketplace (as long as they haven't been placed into your tank yet) and still remain breedable.
No live births. Since fish cannot be removed from the tank, the fish would lay eggs which could be collected by their owner and be sold as singles or in batches (stackable like bugs, flowers, tokens, etc) on the marketplace, traded, gifted or kept. These eggs would: 1. have a chance of not hatching/develping and 2. require specific tank conditions to develop.
No separate tank for breeding, rather placing two or more fish into the tank automatically gives you a chance of them breeding. Having two or more of the same type of fish would have a higher chance of breeding then two different types of fish, but there would still be a chance.
The happier your fish are and the better your tank conditions are increase you chances of the fish breeding. Fish would only breed a few times in their lifetime, if at all. Fish with longer lifespans would breed less and have less offspring than fish with shorter lifespans.