According to the Grey Annals in volume XI of The History of Middle-earth, Morgoth re-established himself in Angband in Valian Year 1495. Valian Years are longer than solar years, so converting this to a precise date is not possible, but 1495 equates to about forty-eight before the Moon and Sun first rose. Of course, we cannot be sure that Morgoth created his Dark Throne immediately, but this dating gives a reasonable estimate of the time of its making.

This dating applies to Morgoth's Dark Throne in Angband, which he occupied only after his return to Middle-earth. He may very well have held an earlier Dark Throne during his time in Utumno long beforehand, but if so, this earlier throne does not come into any tale.

As with Morgoth, we know little of Sauron's Dark Throne beyond the mere fact of its existence (the dating shown here assumes that it existed concurrently with Sauron's Dark Tower). At the very least we can say that it existed during the Second Age (since it's mentioned in the rhyme of the Rings) and that he occupied a Dark Throne - which must surely have been a different one - during the War of the Ring.

The Fellowship of the Ring I 2, The Shadow of the Ring