The position of the Congregation for the Causes of the Saints is that canonizations fall under Papal Infallibility:

The Congregation for the Causes of the Saints: “it is the opinion of the majority of theologians that canonizations done by the Holy Father enter within the limits of his infallible teaching authority.” [2006, letter to the author]

Currently, my theological opinion is the same as stated above by the CCS. But since this has not been defined by the Church, as far as I am aware, what would happen IF canonizations by the Holy Father are not infallible?

Certainly, such a weighty decision by the Supreme Pontiff would not be merely is private opinion, for canonizations are promulgated to the whole Church (even if a feast for that Saint is local). Such a decision at least falls under the non-infallible authority of the Pope. And since it is not a teaching of faith or morals, it would then seem to fall under his temporal authority (over discipline). If infallible, canonizations would be dogmatic facts. Some authors categorize dogmatic facts under the spiritual authority (the Magisterium), but I categorize them under the temporal authority.

If non-infallible, then the same rule would apply to all non-infallible decisions under the spiritual or temporal authority: non-infallible decisions can never err to a grave extent, due to the charism of truth and never failing faith of the Pope, and his unblemished Apostolic See. Thus, no person who deserves condemnation for his or her spiritual life could possibly be made a Saint. So, even IF canonizations are not infallible, they would certainly be non-infallible and free from every grave error.

But this implies that we would not be wrong in venerating a Pope Saint, despite a less than grave error (IF so) in a canonization. For grave errors are absolutely excluded by the prevenient grace of God in the decisions of the Pope on doctrine and discipline. Therefore, the canonizations of John 23, Paul 6, and John Paul II cannot be gravely wrong, and to say otherwise is heresy, as it is contrary to the dogmas of the ordinary universal magisterium (constantly taught since ancient times) and the dogmas of Vatican I. There are no grave errors in the decisions of the Roman Pontiff on doctrine or discipline (that is, in the exercise of the Keys of Peter). For “to this day and forever he [Peter] lives and presides and exercises judgment in his successors, the bishops of the Holy Roman See, which he founded and consecrated with his blood.” [Vatican I]

So the many articles from the website that constantly accuse the Popes and Councils, claiming that canonizations are infallible are wrong. For even IF that were true — and I stress “IF” — there can be no grave errors in canonizations by the Roman Pontiff. And this essentially nullifies most of the weight of the argument claiming that canonizations not only are non-infallible, but supposedly can err gravely. No such grave errors are possible, and the contrary is heresy. Thus, the correctness of these canonizations cannot be gravely wrong. So there is not much difference between the opinion that canonizations are infallible and the dogma that these canonizations, like any decision of the Pope on doctrine or discipline, cannot err gravely.

Ronald L Conte Jr