Fast-growing, bunny-safe vine?

[trinityoaks]

I need recommendations on a fast-growing, bunny-safe vine that will grow in hardiness zone 9a. I want to use it to cover my bunny "barn", which is made of wooden lattice. Since we're renting this place, I will need to have the vines in containers for now, but I can get as many as I need to cover the "barn". I want to use this instead of plastic sheeting to help keep my buns dry in a rainstorm (the "barn" has a wooden-siding roof).

 

[Diamond]

scarlet runner beans! They are called 'runner' beans for a reason, and have beautiful red flowers. They take summer heat quite well and tolerate humidity fairly well.