In my experience, the JFET works as a current source down to appr. 1...2 V drain-source (depends on current). Below that it tends to go resistive, which is not really an issue in this application.
@Zero999 and Benta: indeed. Using a JFET was my first thought as well, but then I quickly realized this would not work properly in the op's use case.
Beyond the variation of the current between JFETs of the same model, which may not be a big problem here (you'd just have to settle for a minimum current, the circuit would work fine for higher currents), you have to consider the characteristic curve of a JFET (Ids vs. Vds) @Vgs = 0 to see that below a certain Vds (which would typically be somewhere between 0.5V and 3V depending on the JFET), the current would drop a lot, defeating the purpose of driving the optocoupler's LED at a somewhat constant current regardless of the supply voltage. You could try selecting a JFET for a minimum acceptable current for the LED at Vds = 0.1V, but good luck finding a proper JFET for this while still limiting the max current to an acceptable level for the LED for the max. Vds (thus max. working voltage).
As a side note, the Vfd of the LED is said to be 1.7V but in the 6N135/136 datasheet I have, Vfd is up to 1.9V max? So 1.8V may not even allow to light up the LED if you're unlucky...