Some argue that the gospel accounts are contradictory concerning when the women arrived at the tomb. Here are the relevant passages:
Now after the Sabbath, toward the dawn of the first day of the week, Mary Magdalene and the other Mary went to see the tomb. (Matthew 28:1
When the Sabbath was past, Mary Magdalene, Mary the mother of James, and Salome bought spices, so that they might go and anoint him. And very early on the first day of the week, when the sun had risen, they went to the tomb. (Mark 16:1-2
But on the first day of the week, at early dawn, they went to the tomb, taking the spices they had prepared. (Luke 24:1
Now on the first day of the week Mary Magdalene came to the tomb early, while it was still dark, and saw that the stone had been taken away from the tomb. (John 20:1
The apparent contradiction is that John says that Mary Magdelene went to the tomb "while it was still dark," while Matthew and Luke say that they went at "dawn."
There are at least two reasonable explanations for the apparent contradiction concerning when the women went to the tomb.
As we can see from these possible explanations, there is no necessary contradiction between the gospel accounts concerning when the women arrived at the tomb.
What would actually be more suspicious is if all four gospel accounts were identical. This would mean that they collaborated, perhaps even conspired, with one another to produce a perfectly harmonized resurrection account.
However, what we see instead is four accounts that have significant differences between them, which points towards the fact that each author simply reported the events that he heard about himself. So, rather than producing doubt, the differences between the gospel accounts should actually make us more confident in the historicity of the resurrection accounts.
Not every witness to an event recalls all of the details perfectly, or in the exact same way, so we should expect various accounts of the resurrection events to differ from one another.
As long as we can provide possibilities for how the various resurrection accounts could reconcile into one coherent narrative, then there would be no irreconcilable, or necessary contradiction. This would then allow us to continue believing in the inerrancy and infallibility of the Bible without any compromise.
It's likely that non-believers won't accept the possible explanations that we provide concerning reconciling the apparent contradictions in the resurrection narratives. However, their refusal to accept these explanations is not based upon the fact that reasonable and possible explanations have been provided, but simply upon the fact that they don't want to believe that there are legitimately reasonable and possible explanations.
Their goal is simply to continue justifying their unbelief in the Bible, regardless of any fact or explanation provided to them. So, we can do our best to provide these reasonable and possible explanations to them, but if they blindly close their minds to them, then we have simply done all that we can do. We should inform them that they are being unreasonable and stubborn, and that they are simply trying to shut their minds to the truth.
Some people have trouble accepting possible explanations to alleged contradictions in the Bible, especially ones that they consider a stretch. For example, Dan Barker, president of the Freedom From Religion Foundation, says this:
I have received numerous replies from Christians who think that these contradictions are either trivial or easily explained. Yet not a single "explanation" has been convincing.
The fact is that there are plausible explanations for every alleged contradiction in the Bible. That there is a plausible explanation for an alleged contradiction does not mean that it is definitely the correct explanation for the alleged contradiction.
However, as long as a possible explanation has been suggested, then it has been objectively demonstrated that there is no necessary contradiction regarding the Bible verses and passages brought up.
When people like Dan Barker say that they don't find a particular explanation for a contradiction "convincing," then that is merely their opinion. A plausible explanation has been suggested that eliminates the necessary alleged contradiction. They simply don't like it, which is not at all a relevant argument against the explanation.
To read more about solutions to Bible contradictions and difficulties, check out Norman Geisler's The Big Book of Bible Difficulties: Clear and Concise Answers from Genesis to Revelation. While we do not agree with some of Geisler's theology, particularly concerning his view of predestination, this book is still an excellent resource. It is thorough and filled with research.
Another book to check out is Tim Chaffey's Demolishing Supposed Bible Contradictions: Exploring Forty Alleged Contraditions, which also answers many alleged contradictions in the Bible.