When was Jesus born?
1)Before 4 BCE.
Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king.
There was in the days of Herod, the king of Judaea, a certain priest named Zacharias, of the course of Abia: and his wife was of the daughters of Aaron, and her name was Elisabeth.
Note: Herod the Great died in 4 BCE.
Wikipedia: Herod the Great
2) After 6 CE.
And it came to pass in those days, that there went out a decree from Caesar Augustus that all the world should be taxed. (And this taxing was first made when Cyrenius was governor of Syria.)
Note: Quirinius (in Greek, Cyrenius) became governer of Syria in 6 CE, ten years after king Herod's death.
The Gospel of Luke mentions the census taken by Quirinius when he was governor of Syria, as part of a census of the "whole world", in connection with the birth of Jesus. However Luke and the Gospel of Matthew date the birth to the reign of Herod the Great, who died in 4 BC, nearly ten years before Quirinius became governor. Most historians argue that Luke is in error.