Not a law per se about cats, but the landlord is obligated to keep the premises in good repair and not allow health hazards to exist. Try calling your local board of health next, reporting it as a health hazard for your daughter. And it should be landlord dealing with the other tenant who is feeding them, not you.
To questioners from West Virginia & New York: Although I am licensed to practice in your state, I practice on a day-to-day basis in Massachusetts. I answer questions in your state in areas of the law in which I practice, and in which I feel comfortable trying to offer you assistance based on my knowledge of specific statutes in your state and/or general principles applicable in all states. It is always best, however, to work with attorneys and court personnel in your own area to deal with specific problems and factual situations.
I'm not sure how your landlord is liable for a feral cat population. Are you saying that the feral cats are on the landlord's property and he is responsible for removing them? I would look for feral cat rescue organizations and see if they can assist you. I would also try contacting your city counsel. Often animal control does not have the resources to devote to this type of thing.
This is not to be construed as legal advice. I do not have an attorney client relationship with you.
Feral cats are generally considered "wild" animals so unless your landlord is doing something to attract them to the property he is not responsible for removing them. A local feral cat rescue may be able to help: http://www.saveakitty.org/
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.