How to calculate capacitance and resistance for this simple A.M. radio?
In actual radios, they use the convenient fact that the carrier frequency is much higher than the modulation frequency.  For example, commercial AM goes down to around 550 kHz carrier (don't remember exactly), but the modulation is limited to 10 kHz at most.  That 55:1 ratio gives you a reasonably wide latitude in making a filter that leaves little carrier without cutting into the real signal.

In your circuit, you want the capacitor voltage to decay little between carrier peaks, but still allow for the falling slope of the highest frequency modulation content.  Set the rolloff frequency of the R-C to about the highest modulation frequency of interest.