Here is my revision of Psalm 50 according to the criteria given here.
Have mercy upon me, O God, according to thy great mercy;
and according to the multitude of thy tender mercies blot out my transgression.
Wash me thoroughly from mine iniquity, and cleanse me from my sin.
For I acknowledge mine iniquity, and my sin is ever before me.
Against thee only have I sinned and done this evil in thy sight,
that thou mightest be justified in thy sayings, and prevail when thou dost judge.
For behold, I was conceived in iniquities, and in sins did my mother get me.
But behold, thou lovest truth; the hidden and secret things of thy wisdom hast thou made manifest unto me.
Thou shalt sprinkle me with hyssop, and I shall be clean; thou shalt wash me, and I shall be whiter than snow.
Thou shalt make me to hear of joy and gladness, that the bones which thou hast humbled may rejoice.
Turn thy face away from my sins, and blot out all mine iniquities.
Create in me a clean heart, O God, and renew a right spirit within me.
Cast me not away from thy presence, and take not thy holy spirit from me.
Restore unto me the joy of thy salvation, and with thy governing spirit establish me.
Then shall I teach transgressors thy ways, and the ungodly shall be converted unto thee.
Deliver me from blood-guiltiness, O God, thou God of my salvation; my tongue shall sing of thy righteousness.
O Lord, thou shalt open my lips, and my mouth shall show forth thy praise.
For if thou hadst desired sacrifice, I had given it: but thou delightest not in burnt-offerings.
A sacrifice unto God is a troubled spirit; a heart that is troubled and humbled God will not despise.
Do good, O Lord, in thy good pleasure unto Zion, and let the walls of Jerusalem be built.
Then shalt thou be pleased with a sacrifice of righteousness, with oblation and whole-burnt offerings.
Then shall they offer bullocks upon thine altar.