When thinking about materials science, it is worth reflecting that the periodic table is very large but we produce very small amounts of most of it. In a bad year a country's annual consumption on Osmium could be smuggled in a small suitcase.
Now they decay into Neptunium. Funnily the more stable Americium delays into the less stable Neptunium, which has a half-life of 2.5 days before by alpha-decay decay into Plutonium with a half-life of 24,000 years. The stable Neptunium has a half-life of 2,144,000 years so that's safe.
Really throw a dental apron over it and the radioactivity should be fine (IAMNAD!!!), and a lead lined box should make it completely harmless. I think your sleep hygiene will have a larger effect on your health.
Now, as a trade good, I don't know how liquid the market is for Americium and how much purity matters, but it is definitely storable.
PS- lead if it can absorb alpha particle becomes Radon, which while not great for you, in trace amounts isn't terrible as many homes have it and their are limits for it etc.
[1] https://www.epa.gov/radtown/americium-ionization-smoke-detec...
That decay also emits a gamma ray as a byproduct.
The energy given off by these gamma rays is actually significant at 59.5 keV. For example, let's assume you have $1500 in americium-241 in your mattress. At $1500/gram, that's one gram. With a specific activity of 3.43 Ci/g, that gram has about 3.66×10^15 decays in a 8 hour night. At 59.5 keV per decay the total gamma ray energy is about 35 J, or 500 mSv for a 70kg person. That's equal to 25 full body CT scans, or the yearly occupational dose limit, every night.
Smoke detectors typically contain about a microgram of americium-241, so that translates to a nightly dose of 0.5 μSv, or a yearly dose of 550 μSv. That's about a quarter of the natural background dose. It's also the amount of radiation emitted by the smoke detector, not what you receive. At an average distance of 8 meters, you'll receive just 1/100th of that.