I would tie-wrap or bungee a couple of poles, such as EMT to the top corners of the frame and parallel to the garage door. I would drape a tarp over that. I would tie the tarp grommets to the EMT to prevent blowing, or I would put the bottom edge of the tarp under the wheels. There should still be plenty of room for air to come in and out.
when hurricane sandy took away our electric, I had the generator set up in the driveway between my truck and my wife's truck (parked side to side 10 feet apart). I stretched a tarp between the racks on the roofs and secured it with some 550 paracord. worked like a charm
.......I now see it's a 1 car driveway you're dealing with, so i'd have to vote for the post directly above mine. i'd frame a little more with EMT and not tuck the tarp under the wheels though. maybe hammer a few pieces into the ground just past the asphalt, like 5' tall to secure the front of the tarp. I get paranoid with flammables near hot exhausts.
Don't forget that you will have to add fuel every 6 to 10 hours typically. Now if the generator is converted to natural gas, that generator bunker in the back yard looks great. However it would not be so good in the front driveway.
In the driveway is really good for when you have to go out and get more fuel. Carrying fuel to the back yard in the rain would be no fun. I have wondered if it would be easy to add a connector to let the car fuel pump pump fuel from the tank to a generator.
As already mentioned, any enclosure type box can lead to problems for a gas generator. Gasoline generators produce a lot of heat when running and the gas in the gas tank can boil!
I once made a nice wood enclosure (I thought) for my gasoline generator - had a ridge vent, had openings on all side just under the slopped roof and I even installed 2 box fans powered off the generator on 2 sides of the enclosure.
As a test I started the generator and set back to watch it - after about 20 minutes I noticed heat waves coming from the roof and then noticed what looked like fumes also. Quickly shutting the unit down I could tell the gas in the tank had been boiling!