Hmm, maybe I should hook up a 9V battery to the speaker, with some resistance, and somehow use an SCR to switch it on and off quickly. Does that sound reasonable?
No, it's totally wrong.
The simplest way is to use a transistor, with a lowish collector resistor say 100R. Then couple it into the speaker with a capacitor. That will stop excessive DC current through the coils but still allow AC to get through. The bigger the capacitor the louder it will be. Start off with 1uF.