Make a "pillow case". I made some pillow case type covers for our daughters chairs. The chairs had been covered in white fabric, and the corners were wearing out. The slip covers matched the drapes in the kitchen. (Drapes were St. Vinney's find. Four of them were put on the windows and the other four were made into chair covers.)
You could make them with one end much longer than the other. And you can make box corners to fit the thickness of the chair back.
And use thick fabric.