It is my experience that conservative Christians who believe in biblical inerrancy can never be convinced that even the smallest contradiction exists in the Bible. Why? Answer: Their faith is not based on evidence but upon the still, small voice that they believe talks to them in their heart (head). If the still, small voice tells them that no contradictions exist in the Bible, then no contradictions exist in the Bible! Period. The fact of the matter is, any and all contradictions can be explained away if one tries hard enough to harmonize them. Mormons, Muslims, Hindus and others do the very same thing with the apparent contradictions in their holy books.
I believe that a more productive discussion with a conservative Christian would involve the following topics:
1. How do you know that the voice you hear “in your heart” is God and not simply…YOU?
2. The majority of scholars, including the majority of Roman Catholic scholars who very much believe in the supernatural and the bodily resurrection of Jesus, reject the claim that the Gospels were written by eyewitnesses or the associates of eyewitnesses. How strong is the evidence for the supernatural claims of Christianity, in particular, the Resurrection, if the four Gospels are not eyewitness sources? Just because all the apparent discrepancies in a story can be creatively harmonized does not prove that the story itself is historically true.