So was Jesus born "in the days of Herod the king" (Matthew) or "when Quirinius was governor of Syria" (Luke)? Herod had been dead at least nine years before Quirinius's appointment.
This will not be news to you, I realise; I just want to see if you try to blather away the contradiction with the usual desperate speculations.
It is you that is speculating. Both Matthew and Luke's accounts are correct. The gospels were written just decades after the events occurred by careful historians. Luke 2:1,2 records: "
Now in those days a decree went forth from Caesar Au·gus′tus for all the inhabited earth to be registered; (this first registration took place when Qui·rin′i·us was governor of Syria." You are basing your claim that Herod's death preceded Quirinius appointment on unproven speculation.
According to the Bible Encyclopaedia Insight on the Scriptures,Vol 2, p.722:
"For a long time this was the only governorship of Syria by Quirinius for which secular history supplied confirmation. However, in the year 1764 an inscription known as the Lapis Tiburtinus was found in Rome, which, though not giving the name, contains information that most scholars acknowledge could apply only to Quirinius. (Corpus Inscriptionum Latinarum, edited by H. Dessau, Berlin, 1887, Vol. 14, p. 397, No. 3613) It contains the statement that on going to Syria he became governor (or, legate) for the second time. On the basis of inscriptions found in Antioch containing Quirinius name, many historians acknowledge that Quirinius was also governor of Syria in the B.C.E. period.
There is uncertainty on their part, however, as to where Quirinius fits among the secularly recorded governors of Syria. Josephus lists Quintilius Varus as governor of Syria at the time of, and subsequent to, the death of Herod the Great. (Jewish Antiquities, XVII, 89 [v, 2]; XVII, 221 [ix, 3]) Tacitus also refers to Varus as being governor at the time of Herods death. (The Histories, V, IX) Josephus states that Varus predecessor was Saturninus (C. Sentius Saturninus).
Many scholars, in view of the evidence of an earlier governorship by Quirinius, suggest the years 3-2 B.C.E. for his governorship. While these dates would harmonize satisfactorily with the Biblical record, the basis on which these scholars select them is in error. That is, they list Quirinius as governor during those years because they place his rule after that of Varus and hence after the death of Herod the Great, for which they use the popular but erroneous date of 4 B.C.E. (See CHRONOLOGY; HEROD No. 1 [Date of His Death].) (For the same reason, that is, their use of the unproved date 4 B.C.E. for Herods death, they give Varus governorship as from 6 to 4 B.C.E.; the length of his rule, however, is conjectural, for Josephus does not specify the date of its beginning or of its end.) The best evidence points to 2 B.C.E. for the birth of Jesus. Hence Quirinius governorship must have included this year or part thereof.
Lukes proved accuracy in historical matters gives sound reason for accepting as factual his reference to Quirinius as governor of Syria around the time of Jesus birth. It may be remembered that Josephus, virtually the only other source of information, was not born until 37 C.E., hence nearly four decades after Jesus birth. Luke, on the other hand, was already a physician traveling with the apostle Paul by about 49 C.E. when Josephus was but a boy of 12. Of the two, Luke, even on ordinary grounds, is the more likely source for reliable information on the matter of the Syrian governorship just prior to Jesus birth. Justin Martyr, a Palestinian of the second century C.E., cited the Roman records as proof of Lukes accuracy as regards Quirinius governorship at the time of Jesus birth. (A Catholic Commentary on Holy Scripture, edited by B. Orchard, 1953, p. 943) There is no evidence that Lukes account was ever challenged by early historians, even by early critics such as Celsus."