Years ago I broke the base off of my now wife's favorite bird clock. Now that I got a printer finally, I was able to rectify it! 

I created a base for the clock round close. The overall outer of the clock is a 4-inch diameter so the top has a radius allowing it to nest into the surface. (IT IS NOT FLAT ON TOP). Overall model stands around 182mm tall before the clock.

In case my measurements to the clock were off (and due to a slightly taper) I didn't trust just gluing the model so I used my plastic welder to attach the clock to the new base. 

Overall design is reminiscent of a column design with an extended side on a half circular cylinder. Design is good for the small clock geometry, and is not recommended for heavy applications.