The old-fashioned 'crystal' set might be doable. It requires few parts. It does not necessarily require a power supply. You might make (a) a variable capacitor and fixed coil, or (b) variable coil and fixed capacitor. The parts are not necessarily easy to fabricate.
An unpowered crystal set cannot drive a low impedance load. Therefore headphones should be high impedance, not low impedance. If you only have an 8 ohm speaker, then consider adding a 1-transistor amplifier stage to drive it.