Is there a New York Stae labor law on Written warnings?..AND is there a law of the “time between” one written warning and another?

New York follows the at-will employment law.  See the following from the New York State Dept of Labor.  So, generally, no warning is necessary.  If your employee handbook requires you to be given written warnngs, look for the timelines in there.  Otherwise, you are out of luck.

"Q: Can an employee be fired without due cause?

A: Yes. New York State is an "employment-at-will," state. Without a contract restricting termination (such as a collective bargaining agreement) an employer has the right to discharge an employee at any time for any reason. This also protects the employee's right to resign. An employer may fire an employee for "no reason" - or even for a reason that might seem arbitrary and unfair -- and the employee is equally free to quit at any time without being required to explain or defend that decision.
There are a few exceptions to "employment-at-will." The most significant of these are laws, enforced by the New York State Division of Human Rights, which prohibit discrimination based upon race, creed, national origin, age, handicap, gender, sexual orientation or marital status. For additional information about how the New York State Division of Human Rights proceeds against unlawful forms of discrimination, go to:

www.nysdhr.com.

Other exceptions to the doctrine of "employment-at-will" exist under § 201-d and § 215 of the New York State Labor Law. Section 201-d prohibits an employer from firing an employee for political or recreational activities outside of work, for legal use of consumable products outside of work, or for membership in a union. Section 215 prescribes that no employer shall penalize any employee for making a complaint to the employer, to the Commissioner of Labor, or to the Commissioner's representative, about any provision of the Labor Law. Violation of § 215, can bring a civil fine and separate civil action by the employee. To obtain the text of these statutes, go to:

http://public.leginfo.state.ny.us/menugetf.cgi?COMMONQUERY=LAWS "

Generally, there is no law regarding warnings.  Warnings are done through company policies and handbooks and so forth.  Employees at will like yourself can be fired for good bad or no reason at all.  Therefore, there is no time between one warning and another.  rather, that is something that is up to the employer.