Basically anything that fits!
Keys, wallet, socks, a sandwich. Playing music with stuff in your DemerBox will change the tone and might reduce the bass response. When I travel (this is Demer writing this) I pack my DemerBox into my bag and stuff it full of socks and t-shirts to save space.
When you're using the DemerBox in a pool or at the lake, put a couple beverages inside to keep the speakers facing upright.
The only thing you don't want to put in your DemerBox is water. Cold drinks are fine, but anything that could drip into the internal ports could cause an issue.