My advice would be:
As others have said, there are different standards with each landlord.
Some will not work with you.
What's bad for one landlord may not be bad for another.
Some may want additional security - maybe 2 or 3 months instead of one which is more typical.
Some may want advance rent.
Some may want a guarantor.
So be prepared to pay more money upfront or get a guarantor is what you should be prepared for.
Each landlord is different, therefore consider being upfront regarding your credit; be prepared to show proof of income/pay stubs, possibly have some reference letters handy, possibly offer additional security, possibly pre-pay some of the rent, etc., or consider a guarantor...
Not all landlords are the same. I have worked with clients with bad scores. Have ready all evidence that can prove your responsible at paying bills on time. I have had clients with good scores yet struggled to pay rent. Landlords are people who can be rational working with a good team or broker can help you.
Generally speaking, some managements in manhattan do work with bad credit, depending what is the reason for it. A way to work around it (not every management will allow it though) is getting a strong guarantor, paying extra security / rent upfront or using Insurent. Although, not every management will allow those options and it really depends on the listing.
If you have any other questions ill be happy to help.