I store mine in an extra large locking footlocker in the closet. Since the lock on the footloose is so cheap, I got a padlock and I store the cheap locals keys right on te padlock while keeping the padlock key on my keychain. This prevents anyone who sees the trunk from wondering why I have a padlock on it (like "what's he hiding?") because they see the cheap lock's keys on the padlock and assume the padlock probably came with trunk and he isn't concerned about keeping it locked because the keys are dangling right there. What they don't know is that those keys won't open that padlock, the real keys are with me. This way I am 100% sure no one can get in and see the diapers and I am also fairly certain people will not be suspicious of this crazy lock on this trunk.
"what's in there?"
"oh u know, what isn't in there..Christmas decorations, books, <insert whatever>?"
"why do u have it locked?"
"I don't usually... it came with the lock, see I keep the keys right there.."
In reality no one has ever opened the closet. So I never tested this out but I think it's a good way to lock it up without looking weird. Because if you lock your bedroom door all the time people might think something weird is going on in there...