You will need some down payment even with FHA.
Here are other options:
Seller financing: Talk to sellers and see if they will finance the purchase-- in this market, you may succeed, especially in places like Queens, Bklyn, or SI.
Rent with option to buy: A portion of your rent goes toward the downpayment and when you do close under the option (your option), you get credit for the down payment and use bank financing for the rest.
New construction: Some builders, stuck with inventory, may also offer no money down options.
Pre-foreclosure: Negotiate with the seller (and lender): You may be able to assume the mortgage and pay any seller equity over time via a promissory note or second mortgage.
Don't give up and you will find something.