How exactly will they be helping you? The only way they can assist you is by gifting you money for down payment & closing costs. You'll have to qualify based on your own income & credit.
If the entire down payment is coming from money your parents are giving you, the problem you'll run into is that conventional guidelines say you must have at least 5% of your own money and the rest can be gifted funds from relatives. I strongly suggest that you meet face-to-face with a Loan Officer. These are things you want to discuss with a Loan Officet and see what your options are.
We have several branches in NYC where I make myself available to meet with clients. If you need a Loan Officer experienced in co-op lending, feel free to call me. Good luck!
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Senior Loan Officer
STERLING NATIONAL BANK
310 Crossways Park Drive
Woodbury, NY 11797