Ex cathedra pronouncements are not as rare as some would have you think. Bl. Pope John Paul II did, in fact, have recourse to his infallible magisterium when he defined the bounds of the Church's authority in regard to the sacerdotal ordination of women in his encyclical Ordinatio Sacerdotalis. ("Wherefore, in order that all doubt may be removed regarding a matter of great importance, a matter which pertains to the Church's divine constitution itself, in virtue of my ministry of confirming the brethren (cf. Lk 22:32) I declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgment is to be definitively held by all the Church's faithful.")
That said, I do not know of the Holy Father using this papal prerogative in regard to the Divine Mercy Sunday, nor any of the private revelations of St. Maria Faustina Kowalska. If someone believes that the Holy Father did use his singular privelege, he should post the solemn judgment for all to see.
The infallibility which Our Lord wished His Church to possess and exercise is very closely defined at the First Vatican Council:
"Therefore, faithfully adhering to the tradition received from the beginning of the Christian faith, to the glory of God our Saviour, for the exaltation of the Catholic religion and for the salvation of the Christian people, with the approval of the Sacred Council, We teach and define as a divinely revealed dogma that when the Roman Pontiff speaks EX CATHEDRA, that is, when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his Supreme Apostolic Authority, he defines a doctrine concerning faith or morals to be held by the whole Church, he possesses, by the divine assistance promised to him in blessed Peter, that infallibility which the divine Redeemer willed His Church to enjoy in defining doctrine concerning faith or morals. Therefore, such definitions of the Roman Pontiff are of themselves, and not by the consent of the Church, irreformable. So then, should anyone, which God forbid, have the temerity to reject this definition of ours: let him be anathema."
So, if the Holy Father did not:
1) exercise his office as shepherd and teacher of all Christians,
2) exercise this office in virtue of his Supreme Apostolic Authority,
3) define a doctrine concerning faith or morals,
4) bind said doctrine to be held by the whole Church,
then he did not have recourse to his papal prerogative of infallibility.