If that's your standard, then there is evidence that Mohammed flew on a winged horse to the Temple Mount. Or more close to home, there is evidence in the Gospel of James that Jesus was born in a cave.
If we want to water down the word evidence to your standard, then from now on I'll just qualify it with "good evidence", or "evidence that stands up to cursory scrutiny".
The supernatural claims of the Bible (and a lot of the historical ones) are neither.
That’s not “my standard”.
If you are a member of a jury in a trial, you hear the evidence of the case, including witness testimony.
You then, taking all the evidence into account, decide which side in the case will win.
Sometimes a witness will tell seemingly fantastical tales which actually wind up being true in the final analysis.
If you told the average person hundreds of years ago that we would have heavier-than-air machines today that could fly across this country in less than six hours, most would think you were a lunatic.
Any good scientist will not dismiss things out of hand, but will simply say “I don’t know”.
My favorite supernatural event from the Bible is the “pillar of fire” from Exodus. May sound off-the-charts crazy, but there actually are fire tornados.
http://www.youtube.com/watch?v=rULehi-U5hI
Of course, many times witness testimony will sound very convincing and seem to make perfect sense, and yet turn out to be lies.
The truth is all that matters in the end; the rest is meaningless nonsense.