Referencing New York State not City: For records between 1800 - 1847, I have found it necessary not to rely on internet databases. Try asking the closest public library and historical society if they have any records. Sometimes they have the Family Bible for that family. (I found one that way) Don't forget to ask the county historian. Each county has one. Finally, depending on what religion / denomination they practice, there may be records of christening, baptism, or membership at churches. If you are looking for west of the Hudson Valley close to 1800 it becomes very very difficult if not impossible to find records. That was the frontier until about 1810s or 1820s.