CLYDE:
Clyde seems to be the most popular choice mostly because he fell asleep in class. People think this implies that Clyde is tired from running around all night, but there are two problems with this theory. One, Mysterion doesn't appear until the night after Clyde fell asleep in class. Two, Cartman stays up all night as the Coon and doesn't appear to succumb to his fatigue in class.

Mainly because when Mysterion shows up at the Police Station, they are already familiar with him.

And it's not really all night if they are showing up between 5:40 and 5:45 (as Cartman states The Coon will appear) I think Cartman, at least, goes home early since his whole plan was just to get famous.