What penances do priests do for sins they absolve?
That will depend on the individual priest, who will more than not, take that information to the grave.
We can only guess!
Let me answer with a anecdote from the life of St. John Vianney and we know what penances he did in his lifetime.
In the beginning of his ministry as a confessor, he handed out harsh penances. As the years went by, he started to hand out lighter penances and took up what needed to be done himself!
“The devil does not fear much discipline and instruments of discipline (hair shirts), what he really fears is the reduction of food, drink, and sleep.” - Saint John Marie Baptist Vianney, Curé of Ars (1786-1859)
We can only guess what penances he did for his penitents.
“The life of Jean-Marie Vianney was spent in the confessional”. So said the Abbé Alfred Monnin, who frequently visited the Curé for more than five years, and who became his biographer. Some distinctive features of the care of souls, woven by the patron saint of parish priests in the discreet shadow in which the sacrament of penance is celebrated, were recently gone over by Philippe Caratgé, moderator of the Priestly Society of St Jean-Marie Vianney, in his report to the international congress held at Ars in late January, the papers of which are to be published shortly.
For the Curé d’Ars – one can see from his catechism classes – a good confession must be humble, simple, prudent and complete. It is necessary to “avoid all unnecessary self-accusations, all those scruples that make one repeat the same thing a hundred times, that make the confessor waste time and annoy those waiting for confession”. It is necessary to “confess what is uncertain as uncertain, and what is certain as certain”. The essential is to “avoid any simulation: that your heart be on your lips. You can cheat your confessor, but remember that you will never ever cheat the good God, who sees and knows your sins better than you”. He himself spent little time with those who came to kneel at his confessional, so that there might be time for all. Brief confessions, brief words. Yet there was not one penitent who did not feel the subject of particular concern, of a dedication always ready to take advantage of every minimal opening for the action of the Spirit, who “like a gardener never finishes working the land” (Caratgé), even that of the most hardened of hearts. “For me,” repeated Jean-Marie about the reparation to be asked from penitents, “I’ll tell you my recipe. I give them a small penance, and I do the rest for them.” The thing that counts, said the Curé, is to have at least a little contrition for one’s sins. With perfect contrition one is forgiven “even before receiving absolution”. Therefore “more time must be spent in asking for contrition than examining oneself”.
For the Curé, confession is the unimaginable gift that God brings forth as a surprise to save His endangered children: “My children, one cannot understand the goodness that God had in establishing this great sacrament. If we had had a grace to ask of Our Lord, we would never have imagined asking for that one there. But He foresaw our weakness and our inconstancy in goodness, and His love led Him to do what we would never have dared ask Him”.
Even more, it’s a gift that reveals in the most intimate way the nature of the mystery of the Trinity. Shut up in his confessional, the simple heart of the Curé savored the mystery of the very heart of God in unparalleled manner. The imperfect pardons of men sometimes seem largesse conceded at a high price, made when we want to look good. God’s forgiveness is another thing. “How can we despair of His mercy, since His greatest pleasure is to forgive us”, the Curé wrote. That is why the treasure of divine mercy is inexhaustible, and no one can think of accounting for the gifts of grace. As if they were debts that sooner or later have to be paid, which we can balance by our own works. Because for God Himself to forgive is the greatest bliss. And it is this that makes Him a beggar for man’s heart. “His patience awaits us,” the Curé reassures. More: “It is not the sinner who returns to God to ask Him for forgiveness, but it is God who runs after the sinner and makes him come back to Him”.
The Curé d’Ars and confession
The Church prays for sinners and does penance with them. We all have to share in this, just not priests who hear confessions. The communion of saints is thus made stronger.