In playing for contra dances there are logistical and economic pressures that push for smaller bands. While the older larger bands would often include drumkits, if you're thinking about how to allocate roles among three—or especially two—people you're usually (but not always) going to do without a drummer. Even without a drummer, though, bands often want something in the general direction of a kick drum to provide a thumpy beat on sets that need it. What are the approaches you see?
The most straightforward is for one of the musicians to stamp their foot on the stage or a board, and amplify that. This is best suited for musicians who are interested in more than just stamping out out a downbeat: it doesn't have a huge amount of low-end punch but in exchange the musician can make complex and varied rhythms using both their feet. A French Canadian "one, two, and" beat is a common place to start, but it can be taken much farther. Here's Noah VanNorstrand in Buddy System:
John Cote in Perpetual e-Motion":
Matt Turino in the Mean Lids:
If you want something simple, cheap, and portable, with a consistent thump, analog piezo boxes (ex) can work well. Here's Alex Cumming playing one with Carol Bittenson:
And Claude Ginsberg with KGB:
A more flexible option is the Roland SPD::ONE Kick Pad, which is an electronic instrument. Instead of capturing and filtering the vibrations induced by your stomps it measures how hard you're tapping and uses that to trigger drum sounds. This means you can choose exactly what it sounds like, including a traditional bass drum kick. Here's Guillaume Sparrow-Pepin playing one with Nova, adding some thump to Everest's higher-pitched but more expressive acoustic feet:
Instead of an all-in-one pad you can also combine the brain (sound synthesis module) from an electronic drum kit with a trigger, including homemade ones. If you get the brain used (which isn't hard—a lot of people get electronic drum kits and then abandon them) this is a lot cheaper than a Pad at the cost of carting around more gear. It's especially a lot cheaper if you want multiple pedals for different sounds, because the brain is the main cost. Here's Guillaume again:
Instead of making a trigger you can also buy a beaterless kick pedal like the Yamaha KU-100. This is what I use these days, and is a good fit if you want to play heel-toe to control four pedals with two feet.
One that I've seen very occasionally but wasn't able to find a video of is playing a real kick drum. The main downside is these are very bulky, but as you'd expect they work well and sound good.