With a Leslie speaker the pitch of an instrument is moved up and down by the doppler effect. I was thinking about ways to do this with an acoustic instrument, but most instruments wouldn't be suitable. You need the sound to come out in more or less one place, and you need to be able to spin that. So what about a Leslie Trumpet:

It's like a herald trumpet, with the long section having an airtight rotating right angle joint so the horn can spin around.

Or, what about a Leslie Bagpipe?

Here only the drones spin, and they're all on the same side of the instrument so they vary together. You'd really need to hemp the drones well to keep them from flying off, or you might need to add a clasp.

You might need to put counterweights, to make them take less effort to spin. Probably partial counterweights, since with a perfect counterweight you can't keep it spinning with small motions.