When we were using a portable generator, I bent a 4x4 sheet of aluminum into a tent like shape that sat over the top of it. It worked well for normal rain, but it would have done little in a hurricane.
I don't have pictures of it anywhere and I repurposed the aluminum for something else when I mounted the current generator under the bus.
A quick google search revealed this
https://www.amazon.com/Mr-You-Univer...a-832585401056
For 20 bucks, it might be worth trying.
Anything with an air cooled engine, do your best to not obstruct the air flow of the machine.
And if you're using an open frame generator in a monsoon, good luck.