I am looking for the web site run by New York State that provides the
laws associated with child support (in New York, this comes under the
Child Support Standards Act). It is a requirement that the site be a
site run by the state, not some other organization. Thank you.

Hi! I believe you are looking for this website: 

Division of Child Support Enforcement
http://www.otda.state.ny.us/csms/abouteng.htm

It references Chapter 567 of the Laws of 1989 of the State of New
York.

The following URL will take you to a search of New York State laws on
“child support”:

Search Results – Query: child support
http://caselaw.lp.findlaw.com/scripts/nycodeft.pl?cirestriction=child+support

Of some particular interest, perhaps: 

TITLE 6-A - ESTABLISHMENT OF PATERNITY AND ENFORCEMENT OF SUPPORT
http://caselaw.lp.findlaw.com/nycodes/c108/a17.html

The Child Support Standards Act is laid out in Section 240 of Domestic
Relations:

Article 13, Sections 230-254
http://caselaw.lp.findlaw.com/nycodes/c29/a24.html

and Section 413 of the Family Court Act: 

Part 1, Jurisdiction and Rules of Support
http://caselaw.lp.findlaw.com/nycodes/c42/a27.html

These latter sites are not New York State run, but they are where the
New York State website directs you to for the state’s statute
information.

I hope this information has been helpful to you.