A 143 No.
An attempt to trip someone who is already prone cannot succeed; they cannot be knocked "more prone". The AoO from their attempt to stand up happens before they have risen any appreciable amount, and they are free to continue to stand up after your attack.
An attack of opportunity "interrupts" the normal flow of actions in the round. If an attack of opportunity is provoked, immediately resolve the attack of opportunity, then continue with the next character’s turn (or complete the current turn, if the attack of opportunity was provoked in the midst of a character’s turn).
permits a trip attempt, the feat does not guarantee that success is possible.