DID DAVID AND SOLOMON EXIST? asks Eric H. Cline in a long, good essay at Bible and Interpretation which surveys the current evidence. His take:

So, did David and Solomon exist? It is fair to say that they most likely did, at least if the Tel Dan Stele with its mention of a Davidic dynasty (Beit David) is any indication. However, the jury is still out as to how important they actually were, how large their empires were, and whether the biblical traditions and stories concerning the two men are essentially correct or were concocted later, either in the time of Josiah in the seventh century BCE or even after. Although David and Solomon have successfully overcome the sabotaging nihilism of the 1990s and the early part of the new millennium, the debates about them are still ongoing, with new discoveries impacting the debate as well as benefiting biblical archaeology as a whole.

That sounds about right to me.