I like Judy's answer below. I'd just add that if depending on the specific coop's income requirement formula, you may have to put a larger down payment than the minimum required by the coop to qualify from that coop's perspective. This is because some coops use income formulas based in part on how much your monthly coop obligation is as it relates to your income. So, the large the down payment, the lower your monthly mortgage payment + maintenance and therefore the lower your income can be.
For example, if your mortgage is $1100/mo and maintenance is $500/mo and the formula is $40K + 12 x ( total monthly mortgage + interest), you'd be required to make $59,200/yr - maybe you do; if not, a larger downpayment would reduce the number. Every coop is different, so make sure you're working with an agent who understands them very well, and follow his/her guidance.
Hope that helps! Don't hesitate to contact me directly with more questions.
Diallo J. Stevens
CENTURY 21 Best, Inc.
YouTube Channel: http://www.youtube.com/DialloStevens
Heritgage House Sothebys International Realty