Unless your parent document is on the same domain as the Facebook Like frame, you can't script into it at all, for security reasons. This is the Same Origin Policy. It prevents you not only from detecting the click but also from impersonating the user, forcing them to perform actions (such as Liking you) without their consent.
You can try to place an element on top of the frame to detect clicks, but by intercepting the click you also stop it going through to the frame. About the best you can do is detect a hover over the area of the Like button and remove the covering element, allowing the user to click. This isn't reliable though since it'll catch all mouseovers.