First thing I would need to know about th egenset is it's type of governor/speed controller.
Instability on a diesel set with an electronic governor is usually too much gain on the governor control (PID), try reducing the gain pot slightly and monitor the reaction.
Beware that this can also make matters worse, so baby steps with any adjustments! (mark th eoriginal positions of any pots you change with a marker so that you can return to original settings if it all goes wrong.
If reducing the gain settles the machine down, make sure that you shut it down and do a re-start as reducing the gain can often cause overspeed on starting.
It's always a compromise and it takes time and experience to get it spot on.
Also as someone else mentioned, check the throttle linkages are free moving with no tight spots, check all electrical connections to actuators.
If all else fails, reset the magnetic pick up gap and check the voltage output.
Happy hunting (sic)