Back in May, NY State created a web database that had an index to update deaths from 1957 to 1963. That database has now found its way to FamilySearch. The FamilySeaxh version is easier to use. As earch gives gives spelling variations and also gives the place of residence that you had to hunt for on the NY site.
I suspect that the reason that the index only goes back to 1957 is that is when NY State Department of Health got their first computer. New records have been added quarterly as NY has a 50 year restriction on the death index.
Check out the FS version of the NY death index via this direct link.