We have no information at all about the making of the Narsilion, except to say that, since it describes the making of the Sun, it must by definition have been written during the Years of the Sun. It may have been written immediately after the events it describes, or - especially if we assume that it was composed by an Elf - it may have been composed thousands of years later.

The song contains a great deal of detail about the making of the Sun and Moon, and so it was apparently written by a witness to the events, or at least by an author with access to such a witness. This would seem to imply that it was written in Valinor, though this does raise the question of how a reference to it could be found within the Silmarillion, which was compiled in Middle-earth. The Noldor had already set out from Eldamar when the Sun and Moon were made, so they could not have carried the tale with them. It may have been carried across the Sea by a later traveller - perhaps even by one of the Wizards - and then incorporated into the Silmarillion at the relevant point in the tale.

The Aldudénië, the Lament for the Two Trees, was a work clearly related to the Narsilion, as it told of the Darkening that led to the making of the Sun and Moon. The Lament was known to have been created by Elemmírë of the Vanyar, so it seems conceivable that he also composed the Song of the Sun and Moon as a continuation of the same epic tale. The Narsilion's author is never named by Tolkien, though, so its true authorship must remain in the realm of speculation.