Call the furniture maker to ask if they have covers available for the couch cushion. Since a lot of Mission style furniture is built by small or custom furniture shops, they may be able to construct a cover for your couch or direct you to someone who can.
Take the seat cushion and any pillow cushions you have on the couch to a custom upholsterer and see if he will be willing to build a cover for them.
Sew your own cover for the cushion. If you cannot sew, you can try simply draping a large piece of fabric over the bottom cushion and tucking the ends into the sides, front and back of the couch. Find new pillow cushions to replace the old ones.