I found a full fitted bed sheet 'fits perfectly' on my RV couch.
The elastic corners grab and stay put at the top corners and bottom corners of the couch.
There is just enough extra to tuck in where the couch folds to make it nice and smooth when used as a couch. And when you open it up voila you have a nice fitted sheet on the couch bed!
Sheets come in a plethora of colors now. I found one that matched my interior colors. Everyone always comments how nice they look and how functional my sheet covers are in my MH.
Looks like maybe a twin or full sheet would fit your small couch perfectly.