Nope. The attack happens before they stand up, when they are still on the ground.
If someone is standing up from prone, could you trip them with a melee attack of opportunity used as a trip attack?
Good question, the developers of Pathfinder actually answered this very question in the FAQ section.
Here's the response:
When a prone character stands up and provokes an attack of opportunity, can I use that attack to trip the character again?
No. The attack of opportunity is triggered before the action that triggered it is resolved. In this case, the target is still prone when the attack of opportunity occurs (and you get the normal bonuses when making such an attack). Since the trip combat maneuver does not prevent the target's action, the target then stands up.
—Jason Bulmahn, 08/13/10
Edit: Curses Cheapy!
No. You can't trip someone when they are prone, because they are already prone. The attack happens before the target actually stands thus the bonuses to hit.
Edit: I need to get a lot faster at answering questions.