I think I answered this in another thread, not sure though...
I'm not a resident of NY but was able to get a non-resident NYPL library card by downloading and printing out their application form, filling it out and mailing it to them with a check for $100 and a copy of my driver's license. My card is good for a year.
They sent me a card in the mail. I can then access their web site for downloadable books to get Adobe PDF books. (Unfortunately they don't have ePub available yet--hopefully will someday!) The books will expire 21 days after downloading.
Hope this helps!
dordale