The Landlord Left Town with My Security Deposit -- Now What?
In most states, your landlord should have returned your deposit within the time specified by law (in a few states, landlords must do so within a "reasonable" time).
The usual tenant remedy is to sue in small claims court if the landlord fails to comply. Unfortunately, you are in the position of many tenants who find themselves in different states than their former landlords: It's pretty hard -- in some states impossible, due to small claims court rules -- to carry out a lawsuit from afar.
Even if you go to court and obtain a default judgment against your former landlord -- many states allow service by mail in small claims court -- it won't do you any good unless the fellow still has property or a bank account in New York. Your fondest hope should be that he is still present owner of a building or two.
Unless there's less than a huge amount of money at stake, it's probably not worth hiring a Florida lawyer to enforce the judgment in that state -- that would be a complicated procedure. And unless the former landlord's cousin is a co-owner, it does not matter a whit that he still lives in New York.
In short, it looks bleak. You might try contacting the cousin and making your case. But if moral persuasion does not do the trick, then it's hard to say what will.