Eh. Not nothing. I can think of several scenarios that would change my mind, or at least make me think hard and open myself up to the possibility of changing my mind.
For example, in a similar scenario to the one you posed... Someone waltzes into the hospital, finds someone who is missing an arm, and says "here's your arm back". If the entire arm grow back in front of my eyes, I'd probably investigate the situation for tricks, and then go home and stare out of a window into the rain while drinking some tea and wondering what the hell I just witnessed. But that wouldn't say anything about WHAT supernatural possibilities I might be convinced of.
If I was sane and not intoxicated, and a god appeared in front of my eyes and did some crazy, normally impossible tricks like manifesting a full-grown dragon into the world, then yeah. I'd be pretty damn convinced.
The problem is that you are providing us with hypotheticals that are aren't clearly supernatural. And for what reason? Even the situation you've described/pulled from another source is attempting to sound realistic, when realistic shouldn't be the point, considering it's still fiction.
If you want to ask atheists what will convince us, why stop at ambiguous hospital scenarios when you could have dragons? Dragons are cooler