At Great Compline in the Byzantine Rite, the Prayer of Manasses (another item outside the Canon of Scripture, but still in the appendix to old Vulgate bibles) is prayed; somehow, it found its way into the U.S. Episcopalian 1979 Book of Common Prayer, as a slightly shortened canticle for use at Morning or Evening Prayer especially in Lent and on penitential occasions, and from thence has passed in its abbreviated form (verses 1-2, 4, 6-7, 11-15 only) into the Book of Divine Worship, the nascent Anglican use of the Catholic Church; it is a good penitential prayer, and I used it to-day after confession; here it is, in the Vulgate Latin (from the Perseus Collection) and the 1610 Douay version therefrom, usefully available online:
Prex ManassesDomine Deus omnipotens patrum nostrorum, Abraham, Isaac et Iacob et semini eorum iusto,  qui fecisti caelum et terram cum omni ornatu eorum,  qui signasti mare verbo praecepti tui, qui conclusisti abyssum et signasti terribili et laudabili nomini tuo,  quod omnes pavent et tremunt a vultu virtutis tuae.  et insustentabilis ira super peccatores comminationis tuae,  inmensa vero et investigabilis misericordia promissionis tuae,  quoniam tu es Dominus altissimus super omnem terram, longanimis et multum misericors et paenitens super malitias hominum. tu autem Domine, secundum bonitatem tuam promisisti paenitentiam remissionis peccatorum,  et tu Deus iustorum, non posuisti paenitentiam iustis Abraham, Isaac et Iacob, his qui tibi non peccaverunt.  quoniam peccavi super numerum harenae maris, multiplicatae sunt iniquitates meae.  incurvatus sum multo vinculo ferri et non est respiratio mihi, quia excitavi iracundiam tuam et malum coram te feci, statuens abominationes et multiplicans offensiones.  et nunc flecto genua cordis mei, precans ad te bonitatem, Domine.  peccavi Domine, peccavi et iniquitatem meam agnosco.  peto rogans te Domine remitte mihi, remitte mihi, ne simul perdas me cum iniquitatibus meis neque in aeternum reserves mala mihi,  quia indignum salvabis me secundum magnam misericordiam tuam.  et laudabo te semper omnibus diebus vitae meae quoniam te laudat omnis virtus caelorum et tibi est gloria in saecula saeculorum, amen.THE PRAYER OF MANASSES KING OF IVDA,WHEN HE WAS HELD CAPTIVE IN BABYLON.LORD omnipotent God of our fathers, Abraham, & Isaac, and Iacob, and of their iust sede, (2 Par 33:12)  which didst make heauen and earth: with al the ornamentes of them,  which hast bound the sea with the word of thy precept, which hast shut vp the depth, and sealed it with thy terrible and laudable name:  whom al thinges dread, & tremble at the countinance of thy powre,  because the magnificence of thy glorie is importable*, & the wrath of thy threatning vpon sinners is intollerable:  but the mercie of thy promise is infinite and vnsearchable:  because thou art our Lord, most high, benigne, long suffering, and very merciful, and penitent vpon the wickednes of men. Thou Lord according to the multitude of thy goodnes hast promised penance, and remission to them that haue sinned to thee, and by the multitude of thy mercies thou hast decreed penance to sinners, vnto saluation.  Thou therfore Lord God of the iust, hast not appointed penance to the iust, Abraham, & Isaac and Iacob, them that haue not sinned to thee, but hast appointed penance for me a sinner:  because I haue sinned aboue the number of the sand of the sea. Myne iniquities Lord be multiplied, mine iniquities be multiplied, and I am not worthie to behold, & looke vpon the height of heauen, for the multitude of mine iniquities.  I am made crooked with manie a band of yron, that I can not lift vp my head, and I haue not respiration: because I haue stirred vp thy wrath, and haue done euil before thee: I haue not done thy wil, and thy commandmentes I haue not kept: I haue set vp abominations, and multiplied offenses.  And now I bowe the knee of my hart, beseeching goodnes of thee.  I haue sinned Lord, I haue sinned, & I acknowlege myne iniquities.  Wherefore I beseech disiring thee, forgeue me Lord, forgeue me: and destroy me not together with myne iniquities, neither reserue thou for euer, being angrie, euils for me, neither damme me into the lowest places of the earth: because thou art Lord, God, I say, of the penitent:  in me thou shalt shew al thy goodnes because thou shalt saue me vnworthie according to thy great mercie,  and I wil prayse thee alwayes al the dayes of my life: because al the power of the heauens prayseth thee, and to thee is glorie for euer and euer. Amen.
[* importable means unsupportable - literally, unable to be borne.][Note that "which" is used for "who", as was common; and that, reflecting the Latin usage, sinners are spoken of as sinning "to" God, rather than "against" Him; similarly, the Lord is referred to in verse 7 as being "penitent", that is, forgiving, of the wickedness of men.]
There is also a similar text, a canticle drawn from the fourth book of Esdras (itself notable as supplying the source for the prayer for the dead Requiem æternam - cf. IV Esdras ii, 34f), which may be styled the Prayer of Esdras (IV Esdras viii, 20b-36); I seem to recall it is used somewhere in the Gothic Breviary of the Mozarabic Rite:
Domine, qui habitas in saeculum, cuius oculi elati et superna in aerem,  et cuius thronus inaestimabilis et gloria inconprehensibilis, cui adstat exercitus angelorum cum tremore,  quorum servatio in vento et igni convertitur, cuius verbum verum et dicta perseverantia,  cuius iussio fortis et dispositio terribilis, cuius aspectus arefecit abyssos et indignatio tabescere facit montes et veritas testificatur.  exaudi, Domine, orationem servi tui et auribus percipe precationem figmenti tui, intende verba mea.  dum enim vivo loquar et dum sapio respondeam.  ne aspicias populi tui delicta, sed qui tibi in veritate serviunt.  nec adtendas impie agentium studia, sed qui tua testimonia cum doloribus custodierunt.  neque cogites qui in conspectu tuo false conversati sunt, sed memorare qui ex voluntate tuum timorem cognoverunt.  neque volueris perdere qui pecorum mores habuerunt, sed respicias eos qui legem tuam splendide docuerunt.  neque indigneris eis qui bestiis peius sunt iudicati, sed diligas eos qui semper in tua gloria confiderunt.  quoniam nos et patres nostri mortalibus moribus egimus, tu autem propter nos peccatores misericors vocaberis.  si enim desideraveris ut nostri miserearis, tunc misericors vocaberis, nobis enim non habentibus opera iustitiae.  iusti enim, quibus sunt operae multae repositae apud te, ex propriis operibus recipient mercedem.  quid est enim homo, ut ei indigneris, aut genus corruptibile, ut ita amariceris de ipso.  in veritate enim nemo de genitis est qui non impie gessit, et de confitentibus qui non deliquit.  in hoc enim adnuntiabitur iustitia tua, et bonitas tua Domine, cum misertus fueris eis qui non habent substantiam operum bonorum.
20b Lord which inhabitest the world, whose eyes are eleuated vnto thinges on high and in the ayre: 21 and whose throne is inestimable, and glorie incomprehensible: by whom standeth an host of Angels with trembling, 22 whose keping* is turned in wynde and fire, thou whose word is true, and sayings premanent†: 23 whose commandment is strong, and disposition terrible: whose looke dryeth vp the depthes, and indignation maketh the mountaynes to melt, and truth doth testifie. 24 Heare the prayer of thy seruant, & with thine eares receiue the petition of thy creature. 25 For whiles I liue, I wil speake: and whiles I vnderstand, I wil answere: 26 Neither doe thou respect the sinnes of thy people, but them that serue thee in truth. 27 Neither doe thou attend the impious endeuours of the nations, but them that with sorowes haue kept thy testimonies. 28 Neither thinke thou of them that in thy sight haue conuerst falsly, but remember them that according to thy wil haue knowen thy feare. 29 Neither be thou willing to destroy them that haue had the maners of beastes: but respect them that haue taught thy law gloriously. 30 Neither haue indignation towards them, which are iudged worse then beastes: but loue them that alwayes haue confidence in thy iustice, and glorie. 31 Because we and our fatheres languish with such diseases: but thou for sinners shalt be called merciful. 32 For if thou shalt be desirous to haue mercie on vs, then thou shalt be called merciful, to vs hauing no workes of iustice. 33 For the iust which haue manie workes layd vp, of their owne workes shal receiue reward. 34 For what is man, that thou art angrie with him: or the corruptible kinde, that thou art so bitter touching it? 35 For in truth there is no man of them that be borne, which hath not done impiously, and of them that confesse, which haue not sinned. (3 Kings 8:46 / 2 Par 6:36) 36 For in this shal thy iustice be declared, and thy goodnes, o Lord, when thou shalt haue mercie on them, that haue no substance of good workes.
[* ke(e)ping - i.e. service: their service takes the form of wind and fire (cf. Heb. i, 7).]
[† premanent- utterly fixed and abiding (from præ + manere), that is, certain.]
I have regard for both these prayers, since they give utterance to the power and majesty of the Lord, and speak accurately of the confusion and penitent prostration of the sinner before God (coram Deo).