In my studies of Islamic Theology I have come across a doctrine of the replacement of sins for good deeds.
“Except for those who repent, believe and do righteous work. For them Allah will replace their evil deeds with good. And ever is Allah Forgiving and Merciful.” 25:70
I do not know of and cannot find any similar doctrine in Christian Theology. Does it exists?
[Note: Some articles I read but couldn't find any similar doctrine in are: Forgiveness (Gods Forgiveness), Repentance (Christianity), Repentance in Judaism, Hamartiology, Christian Views on Sin, Reconciliation (theology), Atonement in Judaism, Salvation in Christianity, Ransom Theory of Atonement, Recapitulation theory of atonement, Satisfaction theory of atonement, Moral influence theory of atonement, Penal substitution, Among others. I of course looked at the Judeo-Christian tradition and not only Christian Doctrine.]
Commenting on ayah 70, Ibn Katheer writes in his acclaimed tafseer: "Imam Ahmad recorded that Abu Dharr said, "The Messenger of Allah said: I know the last person who will be brought forth from Hell, and the last person who will enter Paradise. A man will be brought and it will be said, "Take away his major sins and ask him about his minor sins." So it will be said to him: "On such and such a day, you did such and such, and on such and such a day, you did such and such." He will say, "Yes," and he will not be able to deny anything. Then it will be said to him: "For every evil deed you now have one good merit." He will say: "Oh Lord, I did things that I do not see here." Abu Dharr said: "And the Messenger of Allah smiled so broadly that his molars could be seen." Imam Muslim recorded it.
Ibn Abi Hâtim recorded that Abu Jabir heard Makhul say, "A very old man with sunken eyes came and said, "O Messenger of Allâh, a man betrayed others and did immoral deeds, and there was no evil deed which he did not do. If his sins were to be distributed among the whole of mankind, they would all be doomed. Is there any repentance for him?'' The Messenger of Allâh said: "Have you become Muslim?" He said, "As for me, I bear witness that there is no God but Allâh Alone, with no partner or associate, and that Muhammad is His servant and Messenger.'' The Prophet said: "Allâh will forgive you for whatever you have done like that, and will replace your evil deeds with good merits." The man said: "O Messenger of Allâh, even my betrayals and immoral actions?'' The Prophet said: "Even your betrayals and immoral actions." The man went away saying 'Lâ illâha illallâh' and 'Allâhu Akbar.'
Imputed righteousness is a concept in Christian theology proposing that the "righteousness of Christ ... is imputed to [believers] — that is, treated as if it were theirs through faith." It is on the basis of this "alien" (from the outside) righteousness that God accepts humans. This acceptance is also referred to as justification. Thus, this doctrine is practically synonymous with justification by faith.
In Christian theology, justification is God's righteous act of removing the guilt and penalty of sin while, at the same time, declaring the ungodly to be righteous through faith in Christ's atoning sacrifice.
Another concept approaching the one mentioned is Treasury of Merit (props to GratefulDisciple for this find), whereby the believer can obtain good not only from the "righteousness of Christ" and "Christ's atoning sacrifice", but also from the entire Mystical Body of Christ and/or Communion of Saints.
Although these concepts approach the Islamic concept I've come across closer then any of the various theories of atonement I've read, they are not identical. They differ, of course, by relying on an existing pool of righteousness, which is then transferred to the sinner. But both concepts not only account for forgiveness of sins, but seem to impute actually post fact merit that was unearned by the sinner themself in life (despite what other people have commented thus far).
But whereas the Islamic doctrine does not state that (i.e. an existing pool of merit earned by the Mystical Body of Christ/Communion of the Saints) to be the origin of the good credit then given to the sinner in exchange for his sin, neither does it deny that being the case (though, of course, their pool of righteousness would not include the sacrifice of Jesus, since the Crucifixion is not part of their doctrine).
It may be that more similar doctrines have arisen that none of us have identified yet.