For running small (2000 to 2800) suitcase type inverter generators, I use a plastic bin. The exhaust end is cut out larger than the entire grilled area on generator, and I keep the exhaust end of generator as close to the cut-out as possible (some of the original shipping foam blocks, glued inside the bin, help 'locate' it on the generator, so bin doesn't shift around). I'm not worried too much about rain intruding into the exhaust grille, but I don't want the hot air/exhaust getting caught up under the bin.
On the intake end, I cut a smaller opening, low, where it will be lower than the intake grille (I run generators on a couple of 4x4 blocks, so they're up off the ground). The theory is that air will be drawn in the bin opening, then move upward ( a couple of inches), and 'drop' most rain before it goes into the generator intake. I don't want rain being sucked directly into gen cabinet, and running down back side of inverter module.
Since power outages around me usually come with high winds (along with lots of rain), I cut holes in each corner of the bin, just past the rim, and fix tie-down lines (paracord or something similar), with a loop pre-tied on each line. I keep a set of four tent pegs with the bin, and it's quick to site generator, start it, plug in line to house, drop bin onto generato and stretch out each corner line, and push tent pegs in. Has worked well for me, and generators don't mind it a bit...though I wouldn't try it on an open frame generator!
I was even able to find a bin large enough for the Predator 5000, at Walmart. Think it ran about $15.