Hello stilwtr, welcome to allnurses.
I don't live in NY. I have been reading posts here ... It appears that in addition to schools you might also be able to get CNA training at hospitals, nursing homes, etc.
I did a search around the internet for you and did find - STATE NURSE AIDE TRAINING PROGRAM CONTACTS: New York Department of Health, Bureau of Professional Credentialing, Office of Continuing Care, 61 Delaware Avenue, Delmar, NY 12054 518-478-1060
Give them a call, perhaps they can help you.
Let us, or more importantly other New Yorkers, know how you found a class.