Print in place. No supports. Use gentle force to brake eyes rotatable after print.
A thickness of 2.5mm seems sufficient to hold the rotating eyes inside the socket.
But strong children will squeeze them out bare-knuckle :) → .(
Increase the thicknes with OpenSCAD to make it more robust. (Update 2025-01-28: improved scad-file version (v10) here: https://www.printables.com/model/1167405-eye-rolling-smiley-coaster-in-love)
You can do a manual color change in the middle of printing.
Or - if you own a MMU, use OpenSCAD to render all colored parts. (I didn't try that. Let me know if you've done so)
The author marked this model as their own original creation.