Automatically Find the Center of a Circle in Flash CS6?

I'm working with a puppet that needs to have overlapping circles for joints, and I have multiples of them. Having to go in and attempt to manually find the center of every single circle fills me with as much excitement as a lengthy trip to the DMV, and I'm spending more time finding this mythical Perfect Center of a Circle than I am actually finishing the puppet. So, is there anyway that I can automate this process, so that I can optimize my workflow? Script, extension, macro, anything at all? Or if I can't, what are some tips that can help me make this task not feel as frustrating as it is for me currently? My current process is trying to use Guides on 2000% magnification, move them a pixel at a time, hopefully put the Transform marker in the right spot and spin the joints around so they're dead-on center, rinse and repeat with every section.

For context, I'm working with a dragon that has a lengthy tail, but it only needs to be seen from one side of the body and hence I don't need to do anything too fancy, so I feel it could look smoother if I just used symbols with overlapping circular joints.

Help is appreciated!