Nowhere does the Bible mention water badminton.
But how cool would that be?! I assume we're talking about a pool deep enough players have to tread water instead of standing. I found a video of two guys playing in chest-deep water, but I think water deep enough to drown in would be better. And definitely real racquets with long shafts so you can accidentally hit your teammate.
I'm not sure about the shuttlecock. If the feathers got wet, it would be hard to control, but knowing that might make the players work harder to keep it out of the water.
We could think of variations. Instead of racquets, players could use Super Soakers. Maybe the server has to hit while going down a slide. Maybe the inclusion of Labrador retrievers could add something.
Apropos of nothing, since our church meets at a Y and does
water baptisms in the pool, we joke we should just send people down the slides. The Bible doesn't say anything against it, so I think it would be okay.