How can I automatically centre new windows in Yosemite? Is there a setting or third-party app for Yosemite which will make all new windows open in the center of my display? For instance, when I open a new Finder window, or launch an app.

I've found a wonderful app called Spectacle which lets me center windows (and do all kinds of other useful things) using keyboard shortcuts, but I'd like to automate centering if possible.
Can it be scripted using AppleScript ?
Any time your open a new App, it could call a script to center the Windows.
I do not know if this is possible with your tool, but it is with this one:
http://www.irradiatedsoftware.com/sizeup/