[MrForbes]

If the bearing supporting the cylinder has no friction, then it will behave like you want. Also, if it has very little friction, and there is a lot of inertia in the cylinder, it will mostly behave like you want.

When I was a youngster, gyroscopes were mechanical....they had a part that spun very fast, and it was mounted in a gimble, on low friction bearings. Look it up. Maybe you could do something like that.

But my guess is that you might be able to think of other ways to play the game, that don't require so much fun design and fabrication work.