Inspired by Jangles1981's gear coaster, this is a variation with planetary gears. The top and bottom rotate relative to each other, with 4 planet gears attached to the top and driven by a sun gear in the bottom.
You can add an optional outer ring, which is not only useful to prevent your drinks from sliding off the coaster, but it also turns the coaster into a complete gearbox with a ratio of 5:1 between the top and bottom disks.
Here's a video of it in action.
Print the gear four times. Everything should fit together easily, although you may need to ream the holes in the gears if your first layer is squashed too much. The hole should be 5 mm. If you print it strong enough, it should be possible to easily take it apart for cleaning.
For added coolness, print the top and/or bottom parts in a transparent filament.
This needs to be printed accurately for it to run smoothly. Sandpaper can do wonders, but if you don't know where to sand it, a simple trick is to pour abrasive cleaner (Cif or the like) plus a bit of water into the assembly and spin it for a while. This will automatically sand the parts where it is most needed. Rinse and dry it afterwards.
The top was printed at 0.1 mm layers, the rest at 0.2 mm. I used a finer layer height for the top to ensure the center axle came out accurately. It also proved too weak when printed in ABS at 0.2 mm layers.