Wow, as of October 22, NYS is now permitting felons to serve as Executors of Estates by way of A2573A. 

Previously, a Petition for Probate required an Affirmation as to whether the applicant has been convicted of a felony and if they had, they'd be denied Letters Testamentary (appointment as the estate fiduciary). 

According to the Bill's Justification, the purpose of this new law is to respect the decision of the decedent. Specifically, the Justification states:

In most instances the court respects the choices made by the creator of the document and appoints the nominated parties. It is detrimental to grieving families when an individual is prohibited from acting as an executor due to his or her conviction after paying their debt to society.

That being said, this new law is not without any restrictions whatsoever. Specifically, the law enables the Court to nonetheless declare a felon ineligible if their "crime may be adverse to the welfare of the estate, including but not limited to, crimes such as embezzlement or any crime where there was a misappropriation of money or a breach of fiduciary duty."