The first step in researching the legislative history of an amendment to the NY state constitution is to find out when it was adopted and/or amended. This information is found in the annotated Constitution in McKinney's Annotated Laws of New York (Book 2) and the New York Consolidated Laws Service. To find out where a section appears, see the index at the end of the Constitution.
Early Constitutions: The original New York State Constitution of 1777 is posted on the 18th Century Documents page of the Avalon Project Web site and on the website of the Historical Society of the New York Courts. A bibliography of materials concerning the Constitution of 1777 is published in Gibson's New York Legal Research Research Guide 3d, by William H. Manz.
The Constitutions of 1821, 1846, 1894, and 1938 are posted in the "Charters & Constitutions" section of the website of the Historical Society of the Courts of the State of New York.
Amendments: Since 1777, the New York Constitution has been amended in two ways -- (1) by Constitutional Convention or (2) by having the amendment approved twice by the NY State legislature and approved by a general election. Both are discussed below.
Constitutional Conventions: Amendments dating from 1801, 1821, 1846, 1867, 1894, 1915, 1938 or 1967 were adopted via Constitutional Conventions. The text of these amendments, and most of the debates behind them are held at the law libraries of the New York County Lawyers' Association, the Association of the Bar of the City of New York, Columbia Law School and other New York area law libraries. To find out which pages you need (for all but the 1967 Convention), use the green set of volumes published by the New York State Constitutional Convention Committee in 1938.
The website for the Historical Society of The New York Courts also posts a records of Votes Cast For And Against proposed constitutional conventions and amendments between 1821 and 1987.
A bibliography of materials for each of the Conventions is published in Gibson's New York Legal Research Research Guide, 3d by William H. Manz.
Legislation & Elections: The text of amendments enacted in other years were adopted by legislative action and popular election and can be found in McKinney's Session Laws for the relevant years. Some information may be available in the New York State Legislative Annual. An outline of the legislative history can be found by getting the relevant entry from the NY State Legislative Record and Index.
The New York Legislative Service (212-962-2826) can provide additional legislative history materials on these amendments -- including debates, reports and articles that are often not indexed elsewhere. Note: Be sure to ask the Legislative Service to check their list of "Senate Documents" and "Assembly Documents" for reports and other miscellaneous documents.
Alternatively, you can get the bill number at the end of each section in McKinney's, something of a legislative history from the NY Legislative Digest (formerly the Record) and try to contact sources for this material on your own.
Most of the materials mentioned here are available in the City Hall Library in Manhattan, the New York State Library, the library of the Association of the Bar of the City of New York and the library of the New York County Lawyers' Association. The latter four libraries will make copies and fax. However, if there's research involved, your best bet is to call the New York Legislative Service (212-962-2826), which specializes in New York legislative research.
The classic work on the early history of the New York Constitution is Charles Z. Lincoln's five-volume The Constitutional History of New York from the Beginning of the Colonial Period to the Year 1905, Showing the Origin, Development, and Judicial Construction of the Constitution which is available on the New York State Library's Digital Collections page. Other important works are J. Hampden Dougherty's Constitutional History of the State of New York (1915) and Robert A. Carter's New York State Constitution: Sources of Legislative Intent. Search Worldcat to find libraries that hold these books. Alternatively, all three books are available in electronic format in the subscription-based New York Legal Research Library on HeinOnline.
For a more contemporary perspective on the New York Constitution, see Peter Galie's The New York State Constitution: A Reference Guide (Greenwood Press, 1991), Gibson's New York Legal Research Research Guide 3d, by William H. Manz and/or Robert A. Carter's Legislative Intent in New York State.