Can you take a picture of the sofa frame so we can get a better idea of what you're asking??? I think better with pictures! ;-)

Have you seen mikeytitan's rice sack thread? Maybe you could do something similar, especially since you want it to be portable. I posted a link below.
kathy

Here is a link that might be useful: Mikey titans rice sack on door thread

Thanks for the link. Your link made me realize that I don't have to have have soil all over the frame to have a vine grow all over the frame. If I could rig up something under the seat that would hold the soil, (and there's plenty of room there and it would be well hidden), then the vine would just climb all over the frame. I was originally thinking of attaching some kind of coco fiber or sphagnum moss all over the structure. That wouldn't be necessary. I won't be moving it very often. Perhaps I could just place some pot under the frame, and when they have to be moved, someone will hold the pot while someone else holds the frame.

Now all I have figure out is what to attach to the inside to hold the soil. Also, what plant would be best to show the shape of the sofa and chair. If I lived in a warmer climate, creeping fig would be idea. Is there a plant like that, that would grow in 6-7? I have vinca minor that I was going to give away, could vinca minor be used for a topiary?

Years ago, I saw where someone had made a sofa-shaped frame, filled it with soil, put sod on, and had a grass couch. I would think any groundcover would be cool.