Well you have a couple options. If you have a car without a spare tire, you could see about purchasing the spare tire foam, not sure how but I imagine you could do it somehow, which would leave you a wheel well. If you want it to be 'hidden', then your only other option seems to be to get rid of the foam itself. Otherwise, you could use something like a car organizer and put whatever emergency supplies you want in there. Alternatively, if you don't use the backseat, you could put something on the floor of the backseat (behind driver side only).
I am thinking of cutting off the deep part of the foam that goes into the spare tire. Looks like that part is not needed for strength.