The story of King David is recounted in 1 Samuel 16-31 and 2 Samuel 1-24.
Many of the Psalms are headed "Psalm of David" and he was taken to be the composer of the entire Psalter. Because of this presumption, King David's attributes are a harp and whatever signifies royalty at the time of the painting. For most of the high middle ages that means a crown, as in the first image at right. However, in the first millenium David's kingship can be expressed by such signifiers as standing under an imperial arch (example) or sitting on a throne (as in the second picture at right, which bears a strong resemblance to this 2nd/3rd century image on a probably non-Christian sarcophagus).
As for the harp, it is often pictured as the kind of lyre seen in the second picture at right. Sometimes it can be a "psaltery," a box with strings over a sound hole as in the first picture at right or this Renaissance example.
Instead of a harp, one ivory book cover asserts his authorship by placing him on a throne dictating to four scribes.
Prepared in 2014 by Richard Stracke, Emeritus Professor of English, Augusta University, revised 2015-10-21, 2017-04-10.