I printed the base out of TPU, but it could be printed out of anything, really.  Would recommend gluing some rubber bumper on the bottom if printing out of hard plastics, and clear coating if using PLA to make it last longer.

The inner parts are printed in PLA.  The pawprint and squirrel are inverted so that the top of the final coaster will have your bed texture on it.  

The area around the squirrel's tail is tight and you may have to trim a little to get it to fit properly.  I used a 4.5mm piece of red filament for the squirrel's eye.