Although the vast majority of co-ops do require 20% down, there are some that will take less. You just have to find them! Your best bet would be to have an agent help you. Co-ops that require 20% down will not waiver no matter what.
Another option for you would be to buy a co-op straight from a sponser. A sponser is an individual/investor who owns all the co-ops that went unsold in a co-op building when said co-op first came to be. When you buy from the sponser you do not have to go through a board approval process and can use any down payment the sponser is comfortable with and that can be negotiated.
Another option would be for you to purchase a condo. With condos there is no minimum down payment requirement. Your down payment would be based on your qualifications and could be as low as 3.5%. You can even go with no money down if you are a qualifying veteran.
I am an agent in Brooklyn, if I can be of further assistance to you please let me know. Good luck!
Mitchell S. Feldman
Associate Broker/ Director of Sales
Madison Estates & Properties, Inc.
Office: (718) 645-1665