You need to go to one of few places in New York state that has the Vital Index. It was started (slowly) by state mandate in 1880. If, and only if, the record was forwarded to the state it might be in the index. The index does not include NYC and other cities came on later. NY State explains it in more detail and you can search online for mor information.

The index goes by year and look up the last name. It will give a date, place, and most importantly the file number.

With a file number you get to spend 22 (in 2013) bucks but at least there should be something back for your money.

I have used it to locate birth, marriage, and death. But as said before, in the early years towns did not do so until later. With the file number comes the date and place and first name or initials. If a birth it might state "F" or "M".

Schenectady in 1891 was limited in the early years when I was looking for family.