You'll find St. Cyprian espousing a view of papal primacy that comes remarkably close to how Orthodox Christianity has generally understood the role of the Bishop of Rome in the Universal Church, that is, he is the first bishop to whom the college of bishops owes great deference in his witness to the Orthodox faith insofar as his doctrinal orthodoxy (and the church of Rome) is recognised. Scholarship (as distinct from amateur internet "apologists") i dare say, bears a resounding mark of unanimity on this important feature of St. Cyprian's ecclesiology. Let me give you a few such quotes which convey the mind of this important Father in witnessing to one of the most ancient beliefs about the primacy of Peter, keeping in mind that some of these sources are Roman Catholic:
"In a letter to Cyprian, Firmilian endorsed everything the bishop of Carthage had said and added a few strokes of his own...Recalling the earlier dispute about the date of Easter, he upheld the practice of Asia Minor by commenting that, in the celebration of Easter and in many other matters, the Romans did not observe the practices established in the age of the Apostles, though they vainly claimed apostolic authority for their aberrant forms. The decree of Stephen was the most recent instance of such audacity, an instance so grave that Firmilian ranked Stephen among heretics and blasphemers and compared his doctrines and discipline with the perfidy of Judas. The Apostles did not command as Stephen commanded, Firmilian wrote, nor did Christ establish the primacy which he claimed...To the Roman custom, Firmilian, like Cyprian, opposed the custom of truth, ‘holding from the beginning that which was delivered by Christ and the Apostles.’ And, Firmilian argued, by his violence and obstinacy, Stephen had apostacized from the communion of ecclesiastical unity; far from cutting heretics off from his communion, he had cut himself off from the orthodox and made himself ‘a stranger in all respects from his brethren, rebelling against the sacrament and the faith with the madness of contumacious discord…’ "(Morrison, K 1969, Tradition and Authority in the Western Church, Princeton: Princeton University, pp. 31-32.
“At the same time there is no evidence that he [St. Augustine] was prepared to ascribe to the bishop of Rome, in his capacity as successor of St. Peter, a sovereign and infallible doctrinal magisterium. For example, when in his controversy with Julian of Eclanum he appealed to Innocent, his view was that the Pope was only the mouthpiece of truths which the Roman church had held from ancient times in harmony with other Catholic churches. Nor was he willing, in practical matters, to surrender one jot of the disciplinary independence of the African church which Cyprian had defended so stoutly in his day (Kelly, JND 1978, Early Christian Doctrines, Harper Collins, San Francisco, p. 419).
"Cyprian is convinced that the bishop answers to God alone. ‘So long as the bond of friendship is maintained and the sacred unity of the Catholic Church is preserved, each bishop is master of his own conduct, conscious that he must one day render an account of himself to the Lord’ (Epist. 55.21). In his controversy with Pope Stephen on the rebaptism of heretics he voices as the president of the African synod of September 256 his opinion as follows:
“No one among us sets himself up as a bishop of bishops, or by tyranny and terror forces his colleagues to compulsory obedience, seeing that every bishop in the freedom of his liberty and power possesses the right to his own mind and can no more be judged by another than he himself can judge another. We must all await the judgment of our Lord Jesus Chirst, who singly and alone has power both to appoint us to the government of his Church and to judge our acts therein’ (CSEL 3, 1, 436).
From these words it is evident that Cyprian does not recognize a primacy of jurisdiction of the bishop of Rome over his colleagues. Nor does he think Peter was given power over the other apostles because he states: hoc erant et ceteri apostoli quod fuit Petrus, pari consortio praediti et honoris et potestatis (De unit. 4). No more did Peter claim it: 'Even Peter, whom the Lord first chose and upon whom He built His Church, when Paul later disputed with him over circumcision, did not claim insolently any prerogative for himself, nor make any arrogant assumptions nor say that he had the primacy and ought to be obeyed' (Epist. 71, 3)."
On the other hand, it is the same Cyprian who gives the highest praise to the church of Rome on account of its importance for ecclesiastical unity and faith, when he complains of heretics ‘who dare to set sail and carry letters from schismatic and blasphemous persons to the see of Peter and the leading church, whence the unity of the priesthood took its rise, not realizing that the Romans, whose faith was proclaimed and praised by the apostle, are men into whose company no perversion of faith can enter’ (Epist. 59, 14). Thus the cathedra Petri is to him the ecclesia principalis and the point of origin of the unitas sacerdotalis. However, even in this letter he makes it quite clear that he does not concede to Rome any higher right to legislate for other sees because he expects her not to interfere in his own diocese ‘since to each separate shepherd has been assigned one portion of the flock to direct and govern and render hereafter an account of his ministry to the Lord’ (Epist- 59, 14)...If he refuses to the bishop of Rome any higher power to maintain by legislation the solidarity of which he is the centre, it must be because he regards the primacy as one of honor and the bishop of Rome as primus inter pares" (Quasten, J n.d., Patrology: Vol.2, Christian Classics, Allen, pp. 375-378)
By the way - would you like to discuss the infallibility of Charlemagne and his successors? :-)
“Paraphrasing Vergil, [Charlemagne’s] court theologians hailed him as the one “on whom alone rests the entire welfare of the churches of Christ”….In a response to a warning not to corrupt Charles, Alcuin replied: “It would be impossible for him to be corrupted by anyone, for he is a catholic in faith, a king in power, a pontiff in preaching, a judge in equity, a philosopher in liberal studies, a model in morals.””(Pelikan, J 1978, The Christian Tradition: A history of the Development of Doctrine, vol. 3, ‘the growth of medieval theology (600-1300)’, University of Chicago Press, Chicago, pp. 51-2).