Are you sure it's a co-op? There are 5 residential buildings on Nassau St. that are not rental. Three are co-op and two are condo. I am thinking you are talking about 150 Nassau, because 65 doesn't have active listings, 71 doesn't have any of this size, 140 and 145 Nassau don't have any active sales, but 150 has several active ones that are large. However, 150 is a condo not a co-op. When you buy in a condo, you don't need board approval. The board has what is called the right of first refusal. They have a right to have you do an application and provide info, but they can't turn you down because if they were to turn you down they would have to purchase it. What you are looking for rather than board acceptance is a waiver of the right of first refusal.
I would recommend you have a professional agent represent you and present your offer and negotiate for you. Many deals are falling through these days for all sorts of reasons, so best to have a pro on your side. Which building is it? I can give you more information on it if you want to let me know which one it is.
212 788-7158 (office)
718 744-7158 (cell)