i thought they found a small house from the David-ic period, about 10 meters or more down. Haven’t read about it, but I’ve seen it at a dig once, don’t recall from where I heard that it was David-ic. The stones were irregular shaped, put together like a Chinese puzzle.
There have been structures from the period but no documents or seals. No contemporary mentions of David or Solomon. The closest mention of David’s name was around a century after the period.