No germanium diode available for small crystal radio -- can active components handle the task?
As others (@Kaz) have noted, a Schottky diode may be a simple and cheap solution. I personally haven't seen a crystal radio made with them, but that can very well be because I have really never checked for such a circuit. By all means that should be your first try.

A germanium diode is best known for two properties:


Low threshold voltage
Relatively high resistance in contrast to silicon diodes, resulting in a more curved characteristic.


The low threshold voltage (essentially 0V!) can easily be reproduced with an active half wave rectifier as shown in the image below (found on Elliott Sound Products).



The operational amplifier is used to eliminate the (rightmost) diode's threshold voltage by inserting the diode within the feedback loop. The positive halve waves are amplified by -1 (\$A = -\frac{R2}{R1}\$), so essentially it is an inverting rectifier. With a sine wave you won't notice the difference as both half waves are symmetric.

The leftmost diode prevents the opamp from being driven in saturation (low rail) during the positive halve input wave. Subsequently the inverting input will act as virtual ground (V- = V+) which stabilizes the circuit.

This circuit only works reliably with a dual power supply as the opamp's output will be driven about 0.6V below ground.