I want to make a storage area under my outside deck stairs, at the cot

Is the generator hard wired? If so, check local code as our hardwired generator had to be a certain distance from the house. If it is only storage for a portable check online for an underdecking, one brand is Under Deck Oasis

You can also enclose the staircase and under the platform with framed lattice. Decide where you want to be able to access the space and make a door out of the framed lattice.

I code allows you to put it under the stairway, Decide how large you want the enclosure to be and put down a cement slab or pavers for a sturdy floor to put it on. You can build it with plywood or whatever you want, pallet boards, whatever. You may want to top coat the wood with something like marine polyurethane to keep the elements from rotting the wood. You may also want to put in some kind of areas to allow air circulation when you are using the generator so that no gasses can accumulate and also to keep the generator from overheating. I would suggest having a solid roof on it to keep more of the elements off the generator.

I see that you have windows on either side of the staircase....local codes may prohibit you from installing your generator under the stairs for this reason... as the generators exhaust may enter the house thru the windows (the code may apply even if you do not plan to have the windows open during operation). The codes will dictate how far away from the structure you need to be to run the generator.

If you plan on using it just to secure and store the generator when you are not there, you will need to protect it from water dripping thru the deck above... there are special channels available to install under the deck to catch and divert water away from the area under the deck (I have seen several of the DIY guys use them when the area under a deck is to be used for entertaining or storage space)

check the manual to see if it recommends a distance from structures. You could still store it under the deck and pull it out when in use.

Possibly with a makeshift lean-to

Have you thought about building a raised floor? That would resolve your problem. Make sure you have enough air space around your generator when it's on...

Usually when generators are running they cannot be enclosed.