I used the cap of a toothpaste bottle on the bottom of my pummer as a stand. This pummer has two LEDs that charge during the day and pulse into the night. The circuit uses a 2.5 volt 10 Farad super capacitor for power, which should have a longer lifespan than a battery. My old pummers continue to tirelessly operate after almost a decade.
Here’s a link to a PDF we worked with Make magazine on if you’re interested in learning more or building one: Pummers Dude! (PDF)