How To Determine Online Who Is The Owner of A Coop ...

propertyshark.com

pshark or acris will only help you if there was a UCC filed. Otherwise, SOL. If you are snoopy, you can go to OHs on the same floor and see if there are newspapers lying around or ask the doorman.

Pshark also has the feature of displaying (based on phone records, I think) names of ppl possibly living in the bldg. If these are names that don't show up on ACRIS on UCC-filings, sometimes googling will reveal which unit is associated with what name.

sometimes the reverse directory has apartment numbers in the buildings

You may get luck with propertyshark, but it is a crap shoot.
The alternative is, and it requires patience, but if it's that important you'll do it; painstakingly open each transaction on the acris pages for the building until you see the unit number.
If you are fortunate enough to find on streeteasy or porpertyshark the last time the unit was closed, even the year, that will shorten your work considerably.