I got one of these covers with my 2KW Honda EU2000i generator from MAYBERRYs a few years back (2008)... This one has the little flap that you open up to better grab the generator handle when lifting...
I see them listed on EBAY for sale all the time for less than $20

Ebay photo on GOOGLE Images
My 2KW Honda Generator sits secured in the tailgate corner of my truck bed. I also have a lockable FOLD-A-COVER brand folding hard plastic panels that completely keeps the generator out-of-sight when not in use.
When I need to use it I just pull it out on the tail gate and fire away...

Roy Ken