The article shows that the statement in Luke 2:2 concerning the census of Quirinius, governor of Syria, can be harmonized with available historical and grammatical data. Various proposed solutions are listed, Quirinius' career is described, and two crucial questions are discussed: 1) when was Quirinius governor of Syria, and 2) when did the census of Luke 2:1-2 take place? the article concludes that, although Quirinius may have governed Syria as early as 8-6 BC, a better solution is to translate protē in Luke 2:2 as "first" or "before." Luke was thus referring to a census taken before that of Quirinius in AD 6.
Brindle, Wayne, "The Census and Quirinius: Luke 2:2" (1984). SOR Faculty Publications and Presentations. 73.