Are there dog friendly places to live in Brooklyn?

Four elderly dogs? You sound like my kind of people

Having even one dog, definitely does make it harder to find an apartment. Like OQ says, a pet deposit probably is effective, but I've never been able to pay one, or been asked to pay one. What I've always relied on is negotiation skills and flat-out talking to people to impress on the landlord and his or her representative that I am a responsible person. Leaning on my job helps: I work with animals and this makes landlords more comfortable. In your case, if you can't do that, lean on how long you've had the dogs and that you've managed them the whole time. And give references.

This is still a renters' market, so you should have some leverage. (And I've gotten supposedly no-pet apartments back when the situation was reversed)

If all else fails, look up the legal definition of "open and notorious".