I drill hole at the ends just big enough to fit a small blade through, then use a jig saw to do most of the cuts, then coping saw/files/sandpaper to finish up. Not easy but a lot easier that just the coping saw I think. I cover the foot of the saw with cardboard first so it does not mar the box finish.
I have cut hole with a jig-saw but I always use a metal cutting blade because of the extra small teeth. Seems to keep the wood from splintering as much. If it's available, the best tool is a scroll saw.