Well, with the family cage tending to mimic a hard top, a standard cover would at least be supported from underneath. I’m sure it would be very loose and floppy compared to a full top, but at least it would not collapse in on itself.
I’ve never seen one specifically made for this purpose, but I’ve never actually looked for one either.
Custom would probably be best, but an expensive experiment too. Buying an inexpensive one first as a test would be my choice. Then you could either modify it or have a new one made knowing the parameters.
Any appendages such as a tire carrier or winch?