Bear,
This type of argument takes a particular kind of logic. Let me explain:
If I were to say, "Prove to me that Hitler wasn't reading '2nd Corinthians' on April 5, 1922." You have to show evidence of everything that WAS occurring to make that case. Even if you show loads of evidence of things that he was doing at the time, the objector could still say "You MUST provide an itinerary of every single moment in time that he was awake that day." However, you can make a strong case for it based on the evidence, but you will never be able to satisfy a stubborn objector, if that makes sense.
So, to directly answer your question, here are some important things to consider:
The claim of the resurrection of Christ is documented outside of the Bible. Pliny the younger and Josephus and Tacitus along with others speak about Christians and some of their beliefs.
The Bible states that there were over 500 eye witnesses, and this was written well within the lifespan of some of those witnesses. The fact that this claim was made is a steep gamble for anyone trying to deceive anyone. The apostles also were eye witnesses and even died to defend that claim. Looking at the lives they lived according to Scripture and history, we see that they--in a worldly sense--gained VERY VERY little. In fact, they lost most of their affluence and influence within the greater Roman empire, and KNOWINGLY did so. The same is true with many of their converts, who willfully gave their lives for what they claimed to be true, accurate, and of which many claimed to be eye witnesses.
The fact that an empty tomb was claimed is extremely important. If the disciples stole away the body of Jesus as the Jews claimed, why were they so willing to die for what they KNEW was a lie from the get-go? Also, if they stole the body away, how is it that the Roman guards were not killed, as is custom when they fail in their duty. How did the disciples roll away the stone without the guards realizing? How is it they stole the body away without suffering even 1 casualty or injury by the hands of the roman guards who would have been trained to lay their lives down for their duty?
If Jesus didn't really, actually die--how could he have faked death on the cross, when the Romans were trained to identify that their job was complete (spear in the side)? How could Jesus have garnered any followers if He was bloody, beaten, and likely--if the non-death theory were true--dying from the crucifixion?
The evidence is circumstantial, but circumstantial evidence, couple with eye witnesses accounts is Gospel (pun totally intended).