S.C.
Normally those kinds of "pet" rescrictions don't apply to smaller, caged animals like gerbils or rabbits. I would talk to your landlord, or simply read the fine print in your lease, and see if it's okay to get him a new pet to ease his grieving. That's the one thing about animals (that you don't have with people)...when they die, you can always get a new one.
EDIT: After re-reading my initial reponse, I can see how some people might have thought I was being a little cavalier about "replacing" the cats. That's not what I meant when I said that when a pet dies, you can get a new one...but it's my fault for how I phrased it. This is part of a PM I sent Jackie to explain my advice a little better and hopefully clear things up for D. as well.
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I was the person that suggested that the mom in the apartment give her son a new pet to help with the grieving process of losing two beloved pets, and I guess I was just wondering why you thought that was such a horrible idea? It's not as if these people gave the cats up because they were bored with them or simply no longer wanted the responsibility. As you said, it was done under duress...not at all a choice (I'm assuming that this woman already tried appealing to her landlord). Which means they are feeling very much the same as if their beloved pets had died. I am a pet owner (dog, rabbit, cats) and love them all very much. I would never consider them "disposable" or any nonsense, but I simply don't see any harm in finding healing through the adoption of another pet. Human beings are irreplacable and so are pets on some level. But my point was that, if your husband were to die, there would be an appropriate amount of time that you would take before ever dating or re-marrying. With animals, it's different. You are not dishonoring anyone's memory by finding comfort with another pet right away. You're providing a good home to an animal that needs it (many shelters have rabbits and guinea pigs as well).
I don't see how doing something like this to give her son comfort in a situation that was nobody's fault is going to send him the "wrong message". A gerbil certainly isn't going to "replace" his beloved cats, but it is something else for him to focus his attention and love on because he is hurting SO badly right now. I just feel like you'd rather he continue to suffer on principle, but maybe I'm wrong.