Weddingbee boards

I just googled "new york state online minister marriage" and the first several links all answer your questions

 But to make your life easier, the answer is no.  NYS is pretty strict about such things.  No online ordinations, and no one day deputizations.  Information from here: http://www.health.state.ny.us/vital_records/married.htm

 Who can perform a marriage ceremony?

To be valid, a marriage ceremony must be performed by any of the individuals specified in Section 11 of the New York State Domestic Relations Law. These include:

• the mayor of a city or village;
• the former mayor, the city clerk or one of the deputy city clerks of a city of more than one million inhabitants;
• a marriage officer appointed by the town or village board or the city common council;
• a justice or judge of the following courts: the U.S. Court of Appeals for the Second Circuit, the U.S. District Courts for the Northern, Southern, Eastern or Western Districts of New York, the New York State Court of Appeals, the Appellate Division of the New York State Supreme Court, the New York State Supreme Court, the Court of Claims, the Family Court, a Surrogates Court, the Civil and Criminal Courts of New York City (including Housing judges of the Civil Court) and other courts of record;
• a village, town or county justice;
• a member of the clergy or minister who has been officially ordained and granted authority to perform marriage ceremonies from a governing church body in accordance with the rules and regulations of the church body;
• a member of the clergy or minister who is not authorized by a governing church body but who has been chosen by a spiritual group to preside over their spiritual affairs;
• other officiants as specified by Section 11 of the Domestic Relations Law.

The person performing the ceremony must be registered with the City of New York in order to perform a ceremony within the New York City limits. The officiant does not have to be a resident of New York State. Ship captains are not authorized to perform marriage ceremonies in New York State.

Yep, we did a Universal Life minister too - and they ARE officially ordained and authorized to perform weddings, so in most parts of NYS you should be good!  In NYC I think you have to get an additional form for them to complete (?) so you should check with your county regardless, but a ULC-ordained minister is still a minister!