N.Y. Comp. Codes R. & Regs. tit. 22 § 500.17 : JUDICIARY — Courts — Court of Appeals — Rules Of Practice — Rules Of Practice —Appeals — Calendar

(a) Notification of argument time and date. When the calendar has been prepared, the clerk of the court shall advise counsel by letter of the date and time assigned for oral argument.
(b) Calendar preferences. A party seeking a preference shall address a letter to the clerk of the court, with proof of service of one copy on each other party. The letter shall state why a preference is needed, why an alternative remedy, such as review pursuant to section 500.11 of this Part or submission without argument, is not appropriate, and opposing counsel's position on the request.
(c) Notification of unavailability. Counsel have a continuing obligation to notify the clerk's office of days of known or possible unavailability for oral argument during the court's scheduled sessions.
(d) Adjournments. Requests for adjournment of a calendared appeal are not favored. A party seeking an adjournment shall address a letter to the clerk of the court, with proof of service of one copy on each other party. The letter shall state in detail why the adjournment is necessary, and why submission on the brief filed and having substitute counsel argue are not viable alternatives, and opposing counsel's position on the request.

N.Y. Comp. Codes R. & Regs. Tit. 22 § 500.17