How to build an arbitrary (one-shot) pulse generator?
Just add another component:

Pick any monostable multivibrator that can generate a pulse with the desired timing characteristics;
pick any (slow) two-channel DAC to generate the two desired, constant output voltages (if one output voltage is always GND, you need only one channel);
use an analog multiplexer (random example: TS12A12511) to switch the output between the voltages.

If the DAC's outputs are too weak, add buffers before or after the switch.