Roving Sign, I'm sure you're referring to the modern type of Lionel box car, as the Virginian, pictured above. The 6464 type is an easy fix by putting some sort of thin rod in the bottom door guide track to keep the door closed. For me, I use small brass rods which I have a film canister full of.
Gluing or taping the door closed is not for me, as sometimes I want to open the door, as I have a fork lift that loads crates into box cars. I've tried several techniques including thinning the width of the upper door guide, which is a lot of work.
The technique that works best for me is removing the box car door and putting a dot of glue on the inside of the box car door - on the left side of the door looking at it is the box car. Or in other words, opposite of the side of door that opens.
The dab of glue when dry acts to prevent easy sliding open of the door via vibration of the train, yet allows the door to still be opened.
Another variation of this technique, is to glue a small piece of styrene inside the door in the same manner. The edge of the thin styrene again, keeps the door from vibrating open, yet is not thick enough to allow the door to be opened.
Another technique is to use electrical tape or some other colored tape to match the box car door, and to cut very thin strips to be adhered to the upper part of the door that goes inside the track. Again, you just want enough friction to keep the door from easily opening by running the train, yet not so difficult to open should you wish to.
The ONLY time I ever tape a door closed is on operating cars, like the walking brakeman car, or the opposite door of the spring-plunger "peek-a-boo" operating box cars.