The gate-source voltage (built in) is probably more than 2V, so even if you ground the gate and use a source follower (the source points up), you won't get 2V. It will also vary with temperature and load (if Rload varies at all).
Three diodes in series will do a better job, making probably 1.5 to 2.2V depending on diode type, temperature and load.
An emitter follower (using a PNP BJT) is more stable, because BJTs have higher gain than MOSFETs, but the voltage will still vary by around +/- 0.2V, depending on setup. If you need it more precise than this, you will need an op-amp or voltage regulator or something like that.
Tim