Compressed air pressure vessels are not rated to the same pressure when hot. Especially aluminum yields much sooner when hot. Steel less so but it is still weaker. In a stirling the materials problem is the high pressure and the high temperature on the hot side. Be careful!
Personally, I would start with a steel scuba tank. The steel they typically use is similar to what is used in high pressure boilers, chrome moly. At room temperature they are rated to 2500+ PSI. At 400 or 500C I don't know but it's going to be way better than a compressor tank.
If you don't want your stirling to explode, don't run it with O2 in the working gas. Nitrogen and hydrogen are cheap and safe, helium is safe and expensive. Draw a hard vacuum in your stirling first, then add the working gas. Low concentrations of oxygen prevent explosions, so you don't need to be too mental about the vacuum but don't use regular air, that's 20% oxygen!
Hydrogen is an excellent working gas and cheap. The only issue with hydrogen is progressive embrittlement. Helium is a close second and is perfect other than cost being totally inert. Nitrogen is a distant third from a performance perspective but cheap and effectively inert.