The NY-715 G2 id number JimmyD mentioned is actually the Haxby number from the "Standard Catalog of United States Obsolete Bank Notes 1782-1866", James A. Haxby, published in 1988. New York issues are covered in Volume 3, with this bank appearing on page 1502.
Haxby includes very minimal information on most banks; for this bank he only mentions that it existed from 1862-1920 and was absorbed by Corning Trust Company.
Other than this $1 note, he also lists a $2 note with the same issue date of Sept. 1, 1862 (NY-715 G4). However, Haxby was not aware of any surviving examples of the $2 note. For notes with known survivors he lists some basic valuation information (far out of date, of course), but doesn't provide a rarity scale.