Transistor Series Regulator calculation
For such a low output current, using a darlington transistor is an overkill. I would recommend the following circuit. There is also a good application note here about how to calculate the necessary resistor values. Basically, Rb should be small enough that sufficient base current flows into Q1. However, if it is too small, then the Zener diode will heat up. In the end you choose Rb as a compromise between base current and losses in Dz.