Overview
There seems no reason why a year in a copyright notice could not be specified with a calendar other than the Gregorian Calander, provided it is made clear what system of dates is being used.
US Law
In united-states law the provision for a copyright notice is in 17 USC 401 which provides that:
(a) General Provisions.—Whenever a work protected under this title is published in the United States or elsewhere by authority of the copyright owner, a notice of copyright as provided by this section may be placed on publicly distributed copies from which the work can be visually perceived, either directly or with the aid of a machine or device.
(b) Form of Notice.—If a notice appears on the copies, it shall consist of the following three elements:
(1) the symbol © (the letter C in a circle), or the word “Copyright”, or the abbreviation “Copr.”; and
(2) the year of first publication of the work; in the case of compilations or derivative works incorporating previously published material, the year date of first publication of the compilation or derivative work is sufficient. ...; and
(3) the name of the owner of copyright in the work, or an abbreviation ...
...
(d) Evidentiary Weight of Notice.—If a notice of copyright in the form and position specified by this section appears on the published copy or copies to which a defendant in a copyright infringement suit had access, then no weight shall be given to such a defendant’s interposition of a defense based on innocent infringement in mitigation of actual or statutory damages, except as provided in the last sentence of section 504(2).
Note that subsection (a) says that the notice "may be placed" -- it is not required. Its only legal effect is that in subsection (d) where it defeats any claim of "innocent infringement".
Note also that while a year is part of the standard form of the notice, no calendar is specified by the law, and presumably any calendar could be used, provided that it was made clear which calendar was meant.
Berne Convention
Under the Berne Copyright Convention, to which almost all countries now adhere, no notice is required, and the term of copyright is not based on the date of publication except for anonymous works and works published under a pseudonym.
History, BA and UCC conventions
Under US law prior to the copyright act of 1976, a copyright notice was mandatory -- omitting the notice on a published work would cause loss of all copyright protection. Under that law the period of copyright was always computed from the date of publication, so the year of publication was essential to determine if a work was currently protected or not, and an incorrect year could also cause loss of protection.
Under the Buenos Aires Convention, and the Universal Copyright Convention countreis were permitted to require a copyright notice, and many did, who were not then adherent to the Berne Convention.
Article III paragraphs 1 of the UCC provided that:
Any Contracting State which, under its domestic law, requires as a condition of copyright, compliance with formalities such as deposit, registration, notice, notarial certificates, payment of fees or manufacture or publication in that Contracting State, shall regard these requirements as satisfied with respect to all works protected in accordance with this Convention and first published outside its territory and the author of which is not one of its nationals, if from the time of the first publication all the copies of the work published with the authority of the author or other copyright proprietor bear the symbol © acompanied by the name of the copyright proprietor and the year of first publication placed in such manner and location as to give reasonable notice of claim of copyright.
Notice that a year is required as part of the notice under the UCC, but as in US law, no particular calendar is specified, and presumably alternate calendars could be sued if this is made clear.
