[...] my major stumbling block so far is a way to create high enough voltages but still keep the robot portable.
My only idea is so far is to have several banks of progressively larger caps be charged in parallel and discharged in series but that seems a bit (extremely?) too much.
If you'd use a Cockcroft-Walton multiplier (which would be extremely inefficient for a coil gun), you'd use progressively smaller caps, as the higher the stage, the less charge is transferred at each blurb.
A single power transistor and a transformer (plus a couple of small caps and a resistor or two) is all it takes to generate a several hundred Volt output with plenty of oomph - and it's the oomph that makes the caps charge quickly.
What's your power source and how high a voltage do you need?