That's no help, as it doesn't address the OP's original question of automating window centering.
I can help you with automatically centering Finder windows with
FinderFix - it's simple to use and works great, but that only helps you when working in the Finder. I'm certain
Keyboard Maestro can do what you want, but I've never used it and it does appear that it would require some configuring on your part.