In the end, we ended up using a coffee cup with some added insulation in place of a driver. We had to use an amplifier to supply enough voltage to generate enough current in the wire to produce considerable vibration that would make audible sound waves.
The permanent magnet and the electromagnet were positioned on the same side of the speaker as well. Motion produced by attracting and repelling the permanent magnet by the electromagnet resulted in vibrations that were emitted on the open end of the cup.
Sympathetic resonance is implicated in our design. That is, the resonance produced by the magnet vibrating at the bottom of the cup spreads throughout the cup and insulation, which causes larger amounts of air to vibrate and come to our ears in what we hear as a sound wave.
The speaker sounds great!