"Although not as well known as Herod the Great, the life of Publius Sulpicius Quirinius is fairly well documented. In 12 BC he became consul in Rome and shortly afterwards was given the task of bringing to order the rebelling Homanadensians of Asia. In 3 BC he became proconsul of Asia and in AD 3-4 he was advisor to Caligula during his campaigns. From AD 6 to AD 9 he was the Imperial Legate of Syria-Cicilia. It is during this time that we know an unpopular census for taxation was held in Israel. After this it appears he retired before dying in AD 21. It would appear that Quirinius was not a governor of Syria until AD 6—far too late for the birth of Jesus, how can that be?
... Another way of resolving the problem is that Lk 2:2, mentions that the Nativity census is the 'first census'. He might be suggesting that there might have been more than one census of which this was the first. It is known that when Quirinius became legate in AD 6 he did order a census for taxation and that this caused an uprising in Judea. Luke himself mentions this in his second book, The Acts of the Apostles (Acts 5:37). Luke makes no attempt to link this census with what he describes as the 'first census' in his gospel account. This has caused some people to wonder if Quirinius might have been a governor of some sorts in this area before. He might then have held a census which could have been described as his 'first census' to distinguish it from this infamous taxation census which happened much later.
Dio Cassius, a Roman writer mentions there were taxes levied during this decade. This involved going back to one's home town to work out what had been left you as an inheritance, and then taxes were demanded based on its value. However, Dio Cassius does not help us with the dates of these taxes.
It has also been suggested that when Quirinius was in charge of subduing the Homanadensians from 10 BC to 7 BC Quirinius could have assumed military governorship of the surrounding provinces including Syria. The argument says that he could have secured an oath of loyalty via a census at any time during 10 BC and AD 3. It is suggested that this census prompted Joseph to go to Bethlehem."1: Clues from Quirinius