Crimson King is correct that the Bible claims there was a Roman Census at the time, but alas, there was not. No such census was taken at the time described, and other censii(sp?) do not list anybody that could be recognized as Jesus. If you have this so-called census, feel free to present it.
The other secular scholars you mention were not contemporaries of Jesus and were only going on what the Christians told them.
About this time there lived Jesus, a wise man, if indeed one ought to call him a man. For he was one who wrought surprising feats and as a teacher of such people as accept the truth gladly. He won over many Jews and many of the Greeks. He was the Messiah. When Pilate, upon hearing him accused by men of the highest standing amongst us, had condemned him to be crucified, those who had in the first place come to love him did not give up their affection for him. On the third day he appeared to them restored to life, for the prophets of God had prophesied these and countless other marvellous things about him. And the tribe of the Christians, so called after him, has still to this day not disappeared.
--Josephus, Antiquities of the Jews, Book 18
Josephus wrote around 90AD, and his passage regarding Jesus is mostly fraudulent. We know this because of several lines of evidence. Firstly, none of the early church fathers mention the reference until Eusebius, who is the likely interpolator. Second, it is highly irregular for a Jew such as Josephus to be lauding such praise onto Jesus as the Messiah. The church father Origen even states that Josephus did not believe Jesus was the Messiah. Lastly, this passage does not fit in with its surrounding passages. If we remove it, the passages seem to flow naturally, and this is broken by the insertion.
...derived their name and origin from Christ, who, in the reign of Tiberius, had suffered death by the sentence of the procurator Pontius Pilate
-Tacitus, Annals 15.44
Tacitus also wrote around the time of Josephus, and thus was no contemporary to Jesus. This small line of text does not confirm the historical existence of Jesus, as it might just as easily be heresay given to Tacitus by Christians.
They (the Christians) were in the habit of meeting on a certain fixed day before it was light, when they sang in alternate verses a hymn to Christ, as to a god, and bound themselves by a solemn oath, not to any wicked deeds, but never to commit any fraud, theft or adultery, never to falsify their word, nor deny a trust when they should be called upon to deliver it up; after which it was their custom to separate, and then reassemble to partake of food—but food of an ordinary and innocent kind.
--Pliny the Younger, personal letter to Emperor Trajan
Pliny the Younger makes no specific mention of the existence of an historical Jesus whatsoever, but rather corresponded with emperor Trajan around 100AD about the beliefs and practices of Christians in Asia Minor and asks the Emperors advice on what to do about them.
On the eve of the Passover Yeshu was hanged. For forty days before the execution took place, a herald went forth and cried, "He is going forth to be stoned because he has practiced sorcery (an admission of his miracles) and enticed Israel to apostasy. Any one who can say anything in his favor, let him come forward and plead on his behalf." But since nothing was brought forward in his favor he was hanged on the eve of the Passover!
--Babylonian Talmud, Vol. 3, Sanhedrin 43a
The Talmud was completed in the 6th century, long after Christianity had gained favor in the Roman Empire. This is not a record of what happened in the time of Jesus, but rather a later explanation to justify the Jewish rejection of Christianity.
The Christians, you know, worship a man to this day—the distinguished personage who introduced their novel rites, and was crucified on that account....You see, these misguided creatures start with the general conviction that they are immortal for all time, which explains the contempt of death and voluntary self-devotion which are so common among them; and then it was impressed on them by their original lawgiver that they are all brothers, from the moment that they are converted, and deny the gods of Greece, and worship the crucified sage, and live after his laws. All this they take quite on faith, with the result that they despise all worldly goods alike, regarding them merely as common property.
--Lucian, The Death of Peregrine. 11-13
Lucian, again, wrote long after the supposed death of Jesus in the mid-2nd century. Although he refers to Jesus as if he existed, he is again going on heresay by Christians. No contemporary accounts are cited and no historical data used.
What benefit did the Athenians obtain by putting Socrates to death? Famine and plague came upon them as judgment for their crime. Or, the people of Samos for burning Pythagoras? In one moment their country was covered with sand. Or the Jews by murdering their wise king?...After that their kingdom was abolished. God rightly avenged these men...The wise king...Lived on in the teachings he enacted.
--Letter of Mara Barsarapion
This is getting closer to contemporary, at 73AD. However, the writer would have likely not known or seen Jesus personally, but rather only have a second-hand account at best. This letter also does not mention Jesus by his name, and in fact contradicts the scriptures. It was the Romans who murdered Jesus, not the Jews. One could argue, though, that it was the Jews who brought him to the Romans and demanded it. In any case, the Jews were guilty of killing many other religious leaders of the time, among which was the Essene Teacher of Righteousness. The letter can refer to any number of people.
Another thing I find odd is that many apologetics websites claim that this letter is housed in the British Museum, yet the Museum website contains no references to it. Can anybody substantiate this?
On the whole world there pressed a most fearful darkness; and the rocks were rent by an earthquake, and many places in Judea and other districts were thrown down. This darkness Thallus, in the third book of his History, calls, as appears to me without reason, an eclipse of the sun.
Thallus, quoted by Julius Africanus, Chronography 18:1
This passage does not mention Jesus by name, nor his crucifixion. It only mentions an earthquake and darkness. We also do not have Thallus' text directly, only the quote by Africanus. However, it is known that Thallus wrote a large compendium entitled Histories, which span from the fall of Troy to the 167th Olympiad. However, the 167th Olympiad ended in 109BC, long before Jesus was born. Nobody knows when Thallus wrote or lived. This passage could refer to any time within the Histories, or any time after in some other unknown work by Thallus. Another problem with the darkness and earthquake during the death of Jesus is that
nobody else mentions it. Thallus is the only one that mentions something like it, but we cannot assign a date to it.
During the time of Tiberius Caesar an eclipse of the sun occurred during the full moon.
--Julius Africanus, Chronography 18:1
Unlike Thallus, we do know that Phlegon wrote around 140AD, long after Jesus was gone. Did Phlegon actually see this eclipse? If not, where is he getting the data from? Even if we grant this, the text is not a direct quote of Phlegon, but is in Africanus' own words. We have a direct quoting of Phlegon by Eusebius. Eusebius quotes the following:
Now, in the fourth year of the 202nd Olympiad, a great eclipse of the sun occurred at the sixth hour that excelled every other before it, turning the day into such darkness of night that the stars could be seen in heaven, and the earth moved in Bithynia, toppling many buildings in the city of Nicaea.
Why is this problematic? Firstly, the fourth year of the 202nd Olympiad equates to 32AD, which could not have been the crucifixion year as it interferes with biblical prophecy. Secondly, the earthquake is said to have happened in Nicea, over 500 miles from Jerusalem, where the Bible claims it happened. Phlegon was misquoted by Africanus (or some later interpolater), and does not refer to Jesus.
Once again, we see there are exactly ZERO contemporary secular mentionings of Jesus. The closest we come is to a letter written in 73AD (possibly after the Gospel of Mark, which poisons the well) that does not refer to Jesus by name. Is this what Christians want to count for evidence? If so, they will have to let Hercules, Zeus, Beowulf, Robin Hood, King Arthur, and many other fictional characters into the annals of history.