Four additional Songs of David were published in More Noncanonical Scripture (edited by Bauckham, Davila and Panayotov (Eerdmans, 2013). Geert Wouter Lorein and Eveline van Staalduine-Sulman provide the introduction and translation for the songs.
David Flusser published a translation of these Psalms and concluded the way David is portrayed has some affinity with the world of the Essenes, the universal tone “accords better with the environment which produced the Biblical Antiquities” (Judaism and the Second Temple Period I, 282).
These psalms make use of earlier canonical psalms as well as prophetic material for example, in 1:14-23 (note the Roman numeral refers to the column rather than the psalm).
Psalm I.14-23 You prophesied by Your spirit through the mouth of Your servant for I have brought nigh the end and You will no longer delay it. 15 From the beginning You swore to David Your servant and You anointed Jesse’s root with Your mercy. 16 You sustained his arm with Your holiness, for he established Your praise up to the ends of the earth. 17 You established his name as a pillar of the world, and as a repairer of a breach and as a re-builder of ruins. 18 The rejected cornerstone, which the builders rejected, rose to be the head of all nations. 19 You made him inherit turban and crown with joy and You called out his name to be praised among all nations. 20 Righteousness and justice You have multiplied in his days and well-being and blessings without number. 21 All the righteous chosen ones shout for joy before Your face, for they rejoice in the <de>sirable la<nd>. 22 By his mouth You sanctified the great Name, and all day long he recites Your powerful songs I 23 You made his greatness (as) the great number of all angels’ and You appointed him king of all nations for ever.
David is called “your servant” and the Root of Jesse, both are messianic titles, Isaiah 11:1 combines a root from the stump of Jesse and the Spirit of the Lord. In I.17 the Davidic figure repairs the ruins, a likely allusion to Isaiah 58:12. In I.18 there is a clear allusion to Psalm 118:22: “the rejected cornerstone, which the builders rejected, rose to be the head of all nations.” In Isaiah 28:6 the Lord himself is a crown of glory for his people, in I.19 the Davidic figure inherits a crown with joy which causes the nations to praise him. Likewise, Isaiah 62:2 the messianic figure will be a “crown of beauty” and royal diadem in the hand of God. In the second psalm, the Davidic figure is a “light for the nations” (2:8) Isa 42:6, Luke 2:31-32, Acts 13:47).
In the third song, the Davidic figure “heals the brokenhearted and binds up the bones of the oppressed, he turns mourning into gladness trembling and fear into great forms of trust.” (IV.1-2). Healing the brokenhearted appears in Psalm 34:18 and 147:3, but also in the good shepherd passage in Ezekiel 34:16 where the Lord himself will shepherd his people and will “bind up the injured.” Turning “mourning to joy” is language drawn from Jeremiah 31:13, a text Johan alludes to in John 16:20.
These examples serve to show the writers of these liturgical psalms used the expectation of an idealized Davidic king who would in some way restore God’s rule to Israel. The nations will acknowledge this Davidic ruler and it will be a time when God’s people will magnify the glory of the Lord in their camps and all idolatry will disappear from the people of the Lord (II.16-19). If it is the case these psalms pre-date the first century, they are more evidence the early Christian movement resonated with Second Temple Judaism as the described Jesus as the son of David and the good shepherd who turned mourning into joy (Matthew 5:4; 9:15; 11:17-18).
Flusser, David, “The Apocryphal Psalms of David,” pages 258-82 in Judaism and the Second Temple Period I: Qumran and Apocalypticism. Grand Rapids, Michigan: Eerdmans, 2007.
Lorein, Geert Wouter; Staalduine-Sulman, Eveline van, “A song of David for each day: the provenance of the Songs of David” Revue de Qumran 22 (2005): 33-59.