I'd start with estimating your worst case charge per cycle (you know t, you know
a (rated) static Icc for the driver so there's that; probably know Qgg for your
FET; have to take a guess at how much of a switching impulse pair's charge you
have to make up). Now figure out what kind of droop you can stand across max
on time (dV) and C=Qsum/dV. Now pad that up some for luck.
Or you could solder a stack of caps up, cut them away one by one until
something starts to stank, and then put a couple back along with a new
driver and FET