How do I pick the right resistor for an optoisolator given a desired current?
the datasheet doesn't give a definitive forward voltage

It does: The 1.15 Volts typical, 1.5 Volts maximum specified at 20 mA is the LED's forward voltage specification: It never is a precise voltage, LED voltages can vary greatly between units even within a single batch.

For calculating resistance for minimum current, in the absence of input Vf versus current graphs in the datasheet, use the minimum forward voltage rating for calculations: Vf falls with decreasing current through the LED, but not linearly as the question indicates.

So, for 1 mA: (12 - 1.15) / 0.001 = 10.85 kOhms, use a standard value resistor of 10k.

Note that even if one uses the maximum Vf from the datahsheet, the  results are 10.5k, not much difference.

Note:

With the CTR of the device specified as 200% minimum, 400% typical, a 1 mA input current would allow a nominal 2-4 mA of Collector Current to flow at the output if there were no other current limiting on the output circuit. This may not be sufficient to hold open the driven relay. 

The input current will need to be increased to meet the required output current for the relay. Hence the above 1 mA "desired" current as specified in the question may well be invalid and irrelevant.