Well this is exciting!
Some parts of two of the New York State Censuses are starting to show up at Ancestry.com.
If you are a subscriber to Ancestry, and you go to BROWSE, CENSUS, then go down until you find: New York State Census Collection, you will see that 1880, 1892 and 1905 show up.
Now don't get too excitied yet, it is in no way complete, but it is a start. The ones that I looked at were only partially presented, for instance, 1892 counties of Broome, Chautauqua, Essex, Herkimer, Lewis, Orleans, Rockland, Schoarie, Warren, Wayne and Not Stated. Of those that I quickly scanned, the condition is very poor to say the least, but I do not believe this is any fault of the scanning process. It looks like the source documents were in poor condition and then filmed poorly. However, "some" of the information can be found and perhaps you will get lucky.
I also took a quick look at 1905. The counties presented are; Lewis, Orleans, Schoharie, Warren, Wayne and Not Stated. The condition of the ones I looked at were generally a little better than the 1892.
I did not look at the 1880 yet, but presume this is from the State copy of the Federal Census and of those that I have used in the past they are a slimmed down version of the National Archives film version, but you should look at it any way because you WILL find discrepencies in data that you have previously located on the 1880 Federal version.