Edit: we don't place much stock in petitions, but here it is from the Remnant.
Your Holiness:
Pope Celestine V (r. 1294), recognizing his incapacity for the office to which he had so unexpectedly been elected as the hermit Peter of Morrone, and seeing the grave harm his bad governance had caused, resigned the papacy after a reign of only five months. He was canonized in 1313 by Pope Clement V. Pope Boniface VIII, removing any doubt about the validity of such an extraordinary papal act, confirmed in perpetuity (ad perpetuam rei memoriam) that “the Roman Pontiff may freely resign.”
A growing number of Catholics, including cardinals and bishops, are coming to recognize that your pontificate, also the result of an unexpected election, is likewise causing grave harm to the Church. It has become impossible to deny that you lack either the capacity or the will to do what your predecessor rightly observed a pope must do: “constantly bind himself and the Church to obedience to God’s Word, in the face of every attempt to adapt it or water it down, and every form of opportunism.”
Quite the contrary, as shown in the annexed libellus, you have given many indications of an alarming hostility to the Church’s traditional teaching, discipline and customs, and the faithful who try to defend them, while being preoccupied with social and political questions beyond the competence of the Roman Pontiff. Consequently, the Church’s enemies continually delight in your pontificate, exalting you above all your predecessors. This appalling situation has no parallel in Church history.
Last year, speaking of Pope Benedict’s resignation, Your Holiness declared that if you felt incapable of exercising the papacy “I would do the same.” On the first anniversary of Benedict’s resignation, you called upon the faithful to “join me in prayer for His Holiness Benedict XVI, a man of great courage and humility.”
With no little trepidation, being under the gaze of the One who will judge us all on the Last Day, we your subjects respectfully petition Your Holiness to change course for the good of the Church and the welfare of souls. Failing this, would it not be better for Your Holiness to renounce the Petrine office than to preside over what threatens to be a catastrophic compromise of the Church’s integrity?
http://remnantnewspaper.com/web/index.php/articles/item/2198-the-year-of-mercy-begins