In response I will reiterate a few of the points made by Keith Mathison in his book The Shape of Sola Scriptura. First, infallibility and inerrancy are not the same thing, nor does the latter necessitate the former. I make inerrant (factually true) statements all the time without being infallible (unable to be wrong). In fact, Catholics and Protestants will agree that the Jewish Scriptures were inerrant despite the obvious fallibility of the covenant people who wrote and revered them (Rom. 3:1-2). The point here is that the Old Testament canon was preserved by the Jews to whom it was delivered without the need for infallibility, either of its leaders or of a council to formally adopt it.
Turning to the actual historical recognition of the canon, Mathison points out that although there were local synods in Hippo (393) and in Carthage (397 and 419) that addressed the issue, Rome did not express its opinion on the subject for another thousand years (at the Council of Florence in 1439 - 1443), and it did not authoritatively define the canon until Trent in 1546. The Catholic objection to Sola Scriptura on the basis of the canon, then, falls flat, for the Western Church existed for 1500 years before doing what Protestants are supposedly incapable of doing, i.e., recognizing an authoritative canon.
How, then, do we who hold to Sola Scriptura discover that Scriptural authority without an infallible body to direct us?
In his article entitled "The Canon of the New Testament," Roger Nicole has argued that the way we recognize the canon is by "the witness of the Holy Spirit given corporately to God's people and made manifest by a nearly unanimous acceptance of the NT canon in Christian churches." The sheep of God hear the Shepherd's voice, Jesus says (even without conciliar decrees to make it official, as Rome must admit).
What role does the church play in all this? Adherents of Sola Scriptura (properly understood) would say that the church, though fallible, has made an inerrant judgment concerning the New Testament canon. This is not tantamount to mere subjectivism, Mathison argues, for "it is an appeal to the corporate witness of the Spirit to the whole communion of saints. The Holy Spirit is the final authority, not the church through which he bears witness and to which he bears witness."