Where to a store propane tank?

Me and my boyfriend have a tiny propane grill (think tiny, then think tinier..), and we have these 16 oz cans of propane that we need to store somewhere. For some reason, my boyfriend won't let us store them outside on the deck (we live on the second floor). Right now, they're just sitting under the stairs in a plastic bag. The only problem is that our cat likes to eat plastic bags, and I don't want him to eat it anymore. We can't watch him 24/7 and tell him not to eat it, so we need a better place to store it. Any suggestions?