Empty cardboard wine boxes are the ultimate for storing coindoors!
I restore pinball cabinets and probably the single most awkward thing to deal with is a coin door. Once removed from a game it is bulky and hard to store till I need to re-install it. Most common wine boxes like those that hold 10 to 12 bottles are ideal. The coindoor slides in end first and the top can be closed or even taped shut. It's a perfect way to avoid damaging a coin door, the box fits perfectly, provides protection and is stackable. Trim must be removed for the coin door to fit on some EMs. I don't work on newer stuff so not as sure if it will work for those but its worth a try. I found an endless supply at my local liquor store and they are more than happy to get rid of them.