Calculating resistance for zener diodes?
When designing a zener circuit I usually try to meet the following requirements:


The zener circuit works without load. This means that the zener diode must be able to dissipate the power that is normally dissipated in the load. Check the datasheet for the zener for maximum dissipated power. A regular small zener diode is often rated for 400mW. At this point you know the zener voltage and its maximum power, therefore you can calculate the maximum current through the diode:  \$I_{Z,max}=\dfrac{P_{max}}{V_Z}\$.
The zener is in its regulating mode when maximum load is attached When a load is attached, the current through the zener is lower as a part of the current flows through the load. However a zener needs a minimum current to 'actively' regulate the voltage across it. For an average zener diode this is around 1-5mA, but again you should check the datasheet for this.
The known maximum load current Of course if the maximum load current is lower than the maximum zener current (from #1), there is no need to stress the zener to its max. As long as the minimum zener current is guaranteed, because otherwise it stops regulating the voltage across it.
Maximum load current From the above it can be determined that \$I_{L,max} = I_{Z,max} - I_{Z,min}\$. Or in words: the sum of load current and zener current must be lower or equal to the maximum zener current.


Now if VS is given, you can calculate the series resistor \$R = \dfrac{V_S - V_Z}{I_L+I_{Z,min}}\$