Is the path a sprite object or even a layer? I'm not familiar with what objects DONT have Opacity, but I think most do.
So basically set up an event
System->On Start of Layout
Action: YourPathObject->SetOpacity to YourPathObject.Opacity-0.5
Increase the 0.5 to make it happen faster, decrease it to make it slower.
Feel free to fine tune with 0.559, 0.3461, ect.
If you find this cumbersome, I recommend looking into a plugin called iTween you can find here on these forums that has a built in opacity tween over time.