King David's reign is traditionally dated as beginning in 1000 BC. His story 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. He is especially associated with Psalm 50 (51 in KJV) (cached), whose title is "Psalm of David, when the prophet Nathan came to him about his affair with Bathsheba" -- the story told in 2 Samuel 12:1-15 (cached).
Because of this presumption of authorship, 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 image at left. 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 this 8th-century example, which bears a strong resemblance to this 2nd/3rd century image on a probably non-Christian sarcophagus). Instead of a harp, one 9th-century book cover asserts his authorship by placing him on a throne dictating to four scribes.
The Calling of David: 1 Sam 16:1-13 (cached)
The Calling of David (angel)David and Goliath: 1 Samuel 17:1-54 (cached)
Wall painting in the catacombs of RomeDavid is Anointed King: 2 Samuel 5:1-4 (cached) and 2:4 (cached)
David's Sin and Repentance: 2 Samuel 11:1-5 (cached), 12:1-15; Ps. 51
David sends for BathshebaAt left, 15th-century Italian painting