While not exactly the seal of King David, this is still nonetheless interesting:

Archaeologists have revealed they have found a Jewish seal from the period of the First Temple, according to Professor Gabi Barkay. The seal was discovered in debris which was taken from the Temple Mount six years ago and is the first time a Jewish artifact from the First Temple has been found, he added.

This being Jerusalem, the article can't help but go on to mention the political shennanigans that surround any attempt to dig in the Temple precincts.