Sola Scriptura In The Third Century

"If then it was from the apostles, as we said above, that this custom took its beginning, we must adjust ourselves thereto, whatsoever may have been their reasons and the grounds on which they acted; to the end that we too may observe the same in accordance with their practice. For as to things which were written afterwards and which are until now still found, they are ignored by us; and let them be ignored, no matter what they are." (Dionysius of Alexandria, Letters, 1, To Stephen)

Elsewhere, he wrote:

"And we abstained from defending in every manner and contentiously the opinions which we had once held, unless they appeared to be correct. Nor did we evade objections, but we endeavored as far as possible to hold to and confirm the things which lay before us, and if the reason given satisfied us, we were not ashamed to change our opinions and agree with others; but on the contrary, conscientiously and sincerely, and with hearts laid open before God, we accepted whatever was established by the proofs and teachings of the Holy Scriptures." (cited in Eusebius, Church History, 7:24:8)

The best explanation for such sentiments is sola scriptura. We don't assume without evidence that Dionysius also believed in the papacy, an infallible magisterium, infallible ecumenical councils, and such. And we don't add a qualifier to his reference to scripture if the text and context don't imply that qualifier. If he only refers to scripture, the best explanation is that he had only scripture in mind, not that he also was consulting oral tradition, an infallible magisterium, an infallible ecumenical council, or some other such source. The issue here isn't how Dionysius could be interpreted. Rather, the issue is how he should be interpreted, which interpretation makes the most sense.

It could be argued that Dionysius and his fellow Christians limited themselves to scripture in the context mentioned in the second passage above only because the relevant extrabiblical material wasn't available in that particular context. It wouldn't follow that there was no such material in other contexts. That's possible, but, again, makes less sense. Dionysius is addressing eschatological issues, and that's an area in which extrabiblical traditions are reported early on to an unusually large degree (e.g., in Papias, in Irenaeus). Furthermore, eschatology has a lot of connections to other areas of theology, so limiting yourself to scripture wouldn't just involve whether you think there's relevant extrabiblical material in the more obviously eschatological contexts. Eschatological implications are often interwoven with areas of theology not typically classified as eschatology. And it's not as though the groups who reject sola scriptura, like Roman Catholicism, have claimed that all of their eschatological beliefs are found only in scripture. Papal decrees and councils, for example, frequently address eschatological issues in some manner (Jesus' second coming, resurrection, the day of judgment, etc.). Think of the many references to eschatological issues in the recent Catechism of the Catholic Church. Why should we think the views of groups like Roman Catholicism and Eastern Orthodoxy are the same as those of Dionysius and his colleagues?

We also have to consider the nature of the world in Dionysius' time and the potential for change later. Notice that he doesn't qualify his comments by allowing for some past infallible papal or conciliar teaching he hadn't learned about yet or some such teaching in the future. He seems unconcerned about that sort of qualification.

In addition to what Dionysius affirms in the passages quoted above, there's the absence of anything like an infallible Pope or infallible magisterium elsewhere in Dionysius' writings. You can read what he wrote here and here.