The answer is three but is more complicated than Fox'a answer.
Fox - in your example in your second weighing when one side goes down you don't know if that's due to a lighter coin being on the light side or a heavier coin being on the heavy side.
To start though call the coins 123456789:
Weighing 1: 123 v 456
Outcome 1a: level..... odd coin is in 789
Outcome 1b: LH down... either heavy coin in 123 or light coin in 456
Outcome 1c: RH down... either heavy coin in 456 or light coin in 123