I would recommend a sealed container with desiccant packs. My concern here is that humidity leads to oxidation (rust). I would absolutely recommend avoiding anything petroleum based, as the vapors will quickly denature rubber compounds. For example-anyone ever see what happens to a turntable mat that has been trapped under the dustcover of an oil or grease lubricated turntable? In the presence of petroleum vapors, the rubber quickly becomes rigid and cracks.
I would recommend a jewelry box with desiccant packs. And don't add foam, that gives of vapors too. If you can't locate desiccant packs, make nice with your local Pharmacist, we throw millions of them away every time we open a new bottle of pills. You'll have to "dry them out" first however, which is nothing more than baking them in an oven for a short while.