Strabo also mentions Quirinius (in this translation his name is spelled “Cyrinius”).

Geography 12.6.5

Now Cremna is occupied by Roman colonists and Sagalassus is subject to the same Roman governor to whom the whole kingdom of Amyntas was subject. It is a day’s journey distant from Apameia, having a descent of about thirty stadia from the fortress. It is also called Selgessus; this city was also captured by Alexander. Now Amyntas captured Cremna, and, passing into the country of the Homonadeis, who were considered too strong to capture, and having now established himself as master of most of the places, having even slain their tyrant, was caught by treachery through the artifice of the tyrant’s wife. And he was put to death by those people, but Cyrinius overthrew the inhabitants by starving them, and captured alive four thousand men and settled them in the neighboring cities, leaving the country destitute of all its men who were in the prime of life

Lastly, Josephus also mentions Quirinius (Cyrenius) on five occasions, and talks about his census.

War 2.17.8

In the mean time, one Manahem, the son of Judas, that was called the Galilean, (who was a very cunning sophister, and had formerly reproached the Jews under Cyrenius, that after God they were subject to the Romans,) took some of the men of note with him, and retired to Masada, where he broke open king Herod’s armory, and gave arms not only to his own people, but to other robbers also.

War 7.8.1

When Bassus was dead in Judea, Flavius Silva succeeded him as procurator there; who, when he saw that all the rest of the country was subdued in this war, and that there was but one only strong hold that was still in rebellion, he got all his army together that lay in different places, and made an expedition against it. This fortress was called Masada. It was one Eleazar, a potent man, and the commander of these Sicarii, that had seized upon it. He was a descendant from that Judas who had persuaded abundance of the Jews, as we have formerly related, not to submit to the taxation when Cyrenius was sent into Judea to make one.

Antiquities 17.13.5

So Archelaus’s country was laid to the province of Syria; and Cyrenius, one that had been consul, was sent by Caesar to take account of people’s effects in Syria, and to sell the house of Archelaus.

Antiquites 18.1.1

Now Cyrenius, a Roman senator, and one who had gone through other magistracies, and had passed through them till he had been consul, and one who, on other accounts, was of great dignity, came at this time into Syria, with a few others, being sent by Caesar to he a judge of that nation, and to take an account of their substance. Coponius also, a man of the equestrian order, was sent together with him, to have the supreme power over the Jews. Moreover, Cyrenius came himself into Judea, which was now added to the province of Syria, to take an account of their substance, and to dispose of Archelaus’s money; but the Jews, although at the beginning they took the report of a taxation heinously, yet did they leave off any further opposition to it, by the persuasion of Joazar, who was the son of Beethus, and high priest; so they, being over-pesuaded by Joazar’s words, gave an account of their estates, without any dispute about it.

Antiquities 18.2.1-2

When Cyrenius had now disposed of Archelaus’s money, and when the taxings were come to a conclusion, which were made in the thirty-seventh year of Caesar’s victory over Antony at Actium, he deprived Joazar of the high priesthood, which dignity had been conferred on him by the multitude, and he appointed Ananus, the son of Seth, to be high priest; while Herod and Philip had each of them received their own tetrarchy, and settled the affairs thereof. Herod also built a wall about Sepphoris, (which is the security of all Galilee,) and made it the metropolis of the country. He also built a wall round Betharamphtha, which was itself a city also, and called it Julias, from the name of the emperor’s wife. When Philip also had built Paneas, a city at the fountains of Jordan, he named it Cesarea. He also advanced the village Bethsaids, situate at the lake of Gennesareth, unto the dignity of a city, both by the number of inhabitants it contained, and its other grandeur, and called it by the name of Julias, the same name with Caesar’s daughter.

As Coponius, who we told you was sent along with Cyrenius, was exercising his office of procurator, and governing Judea, the following accidents happened…

Antiquities 20.5.2

Then came Tiberius Alexander as successor to Fadus; he was the son of Alexander the alabarch of Alexandria, which Alexander was a principal person among all his contemporaries, both for his family and wealth: he was also more eminent for his piety than this his son Alexander, for he did not continue in the religion of his country. Under these procurators that great famine happened in Judea, in which queen Helena bought corn in Egypt at a great expense, and distributed it to those that were in want, as I have related already. And besides this, the sons of Judas of Galilee were now slain; I mean of that Judas who caused the people to revolt, when Cyrenius came to take an account of the estates of the Jews, as we have showed in a foregoing book.

Josephus and the Gospel of Luke appear to contradict each other about the date of the census.  The four basic options we have to resolve this are:  (1) The Gospel of Luke is incorrect, (2) Jospehus is incorrect, (3) the Gospel of Luke is awkwardly phrased and has therefore been mistranslated or misunderstood, and finally  (4) Quirinius had more than one govenorship of Syria.