There's a non-gen one here. Can't vouch for it though (one user commented "don't work"):
https://ultralightsound.co.uk/product/replacement-power-supplies-for-zero-88-desks/
I find this thread but the other two supplier links (10-out-of-10 and Stage Gear don't work any more).
This page has the part number, which might be useful in searches as the same PSU is used by: Illusion, Jester, Juggler, Leap Frog 48/98, Solution in addition to the Frog series:
https://www.vari-lite.com/global/products/frog-series#_spareparts
There is this non-gen (maybe a ULS one):
https://www.ebay.co.uk/itm/316738459895
There's a Jester thread here:
https://www.blue-room.org.uk/topic/75786-zero88-jester-power-supply/
The OEM model number seems to be SPU41-13D-1 but having a google, other output connectors can be used.
I suspect the Frog only uses the +5V with +12V only for the lamp; I suspect -12V isn't used.