Martin Daly is probably right in suggesting that the New Amsterdam
Reformed Church means a Dutch Reformed Church. He is also right in that
there were and still are many of them. A nice aspect of them is that
the Dutch were meticulous record keepers and virtually all the Dutch
Reformed parishes had records, some dating back to the first half of
the 17th century. New Amsterdam was served by a parish as was Breucklen
(Brooklyn), Bergen (now Jersey City NJ), and so on. Most of the records
antedating about 1800 were published in book form by the Holland
Society in one of the year books between their first book, sometime in
the 1880's I believe, and the 1930's. Most genealogical libraries in
and around New York and many elsewhere in the country will have copies.
If you can't find them, then I your local Family History Center can
probably provide access through microfilm. I noticed, however, in your
query you did not mention a date, decade, or century. That is crucial
to searching, since the DRC records are sorted chronologically after
being sorted by parish.
One nice feature of the DRC records is that the maiden name of the
wife/mother is always used for marriages AND baptism; and the witnesses
are almost always given again with the woman's maiden name.