Because a New York conditional driver's license is only issued to those convicted of driving while intoxicated (DWI), it is unlikely that you will find an agency that is willing to rent a car to you.
Most rental agencies will refuse to rent to anyone who has been convicted of a DWI in the last one to three years.
Even if you find a rental agency that will rent to you, you will probably be forced to provide your own insurance. The agency is unlikely to be willing to accept the potential liability.
With a conditional license, you will not be able to use a car for recreational purposes, limiting the circumstances under which a rental car can be used.
If you have another person with a clean driving record drive the car, most rental agencies will let you pay for the rental car.
Talk to someone at New York State's Drinking Driver Program. They may know of alternative solutions to your dilemma.
