Yes, these four texts can be added with specific verse references:
Prayer of Manasseh
Invocation (v. 1); Ascription of praise, mentioning God’s work in creation, his wrath and his mercy (vv. 2–7); Confession of sin (vv. 8–10); Petition for forgiveness (vv. 11–15a); Doxology (v. 15b)[1]
Song of the Three Young Men (Prayer of Azariah and Song)
The text comprises two distinct sections. The Prayer opens with Azariah delivering a penitential prayer that affirms the exile as just punishment for the sins of Israel (v. 5), with confession that indicts the nation for failing to obey God’s laws and to keep his commandments (vv. 6–8), followed by an appeal for deliverance on the basis of the covenant promises (vv. 11–13), on offering a “soul of contrition and a humbled spirit” (v. 16), and on the basis of God’s wonders and the glory of his name (vv. 19–22)[2].
The Song divides into two parts: verses 29–34 with direct praise beginning with “Blessed are you,” followed by verses 35–66a in which different parts of the creation are summoned to praise the Lord, with verses 35–51 calling upon the heavens and associated entities, verses 52–59 ordering the earth and everything associated with it to join the cosmic choir, and verses 60–66a addressing all people to bless the Lord, concluding with the reason for blessing: “For he has rescued us from Hades and saved us from the power of death, and delivered us from the midst of the burning fiery furnace,” with a call to thank the one whose mercy endures forever[3].
Psalm 51
A penitential psalm, Psalm 51 is structured in a five-part chiasmus plus an addendum, with emphasis on the central plea for forgiveness: “Hide your face from my sins, and blot out all my iniquities”[4]. More specifically: Mercy and pardon (vv. 1–2), with piling up of synonyms: mercy, unfailing love, great compassion; blot out, wash, cleanse; transgressions, iniquity, sin[5]; Confession of sin (vv. 3–6)[5]; Petitionary section with petitions for cleansing (vv. 7, 9), a request for joy (v. 8), petitions for a steadfast spirit and a willing spirit (vv. 10, 12), with another request for joy inserted between them, emphasizing that penitence is to lead to full, joyful restoration[6]; and Prayer for Zion (vv. 18–19)[5].
Psalm 106
While not explicitly detailed in the search results with verse-by-verse breakdown, the song divides into two formally distinct parts, with verses beginning with “Blessed are you” and statements about praise and exalting God highly[3], followed by communal acknowledgment of sin and petition for restoration—demonstrating the ascription, confession, and petition pattern.
[1] Reidar Hvalvik, “Prayer of Manasseh,” in Dictionary of New Testament Background: A Compendium of Contemporary Biblical Scholarship (Downers Grove, IL: InterVarsity Press, 2000), 821.
[2] Peter W. Flint and C. J. Patrick Davis, “Introduction to the Prayer of Azariah in the Fiery Furnace and the Song of the Three Young Men,” in Early Jewish Literature: An Anthology, ed. Brad Embry, Ronald Herms, and Archie T. Wright (Grand Rapids, MI: William B. Eerdmans Publishing Company, 2018), 1:67.
[3] James C. VanderKam, An Introduction to Early Judaism (Grand Rapids, MI; Cambridge, U.K.: William B. Eerdmans Publishing Company, 2001), 134.
[4] David A. Dorsey, The Literary Structure of the Old Testament: A Commentary on Genesis–Malachi (Grand Rapids, MI: Baker Academic, 2004), 178.
[5] Robert G. Hoeber, Concordia Self-Study Bible (St. Louis: Concordia Pub. House, 1997). [See here, here, here.]
[6] Robert L. Jr. Hubbard and Robert K. Johnston, “Foreword,” in Psalms, ed. W. Ward Gasque, Robert L. Hubbard Jr., and Robert K. Johnston, Understanding the Bible Commentary Series (Grand Rapids, MI: Baker Books, 2012), 228.