Number the coins 1-9. Begin by weighing 1, 2, and 3 against 4, 5, and 6. If they don’t balance, then the counterfeit coin is in the lighter group. If they do balance, then it’s among the three unweighed coins.
Having narrowed the field to three suspect coins, you can apply the same principle in the second weighing. Put one coin in each tray; if they don’t balance, the lighter coin is counterfeit, and if they do, the third suspect must be light.
J.E. Littlewood observes that a similar puzzle wasted 10,000 scientist-hours of work during World War II. “There was a proposal to drop it over Germany.”