rabbit cage plant cover

Okay heres the story. i am about to get rabbits (2) and i live in Texas. I have probably a 200-250 sq foot enclosure that i have made. it is at the back of my property with lots of trees and much short, dead grass. my dad does not like the idea of me having rabbits but i have convinced him. I was thinking about gowing vines on the fence ( only 1 width high of chicken wire) just so it becomes less of an eyesore. Species, ideas, tweaks?

Nice idea, where I am, I would grow hops or a kiwi vine or two, but Texas? I dunno. There must be a regionally appropriate fruit tree nursery that could advise you.

One width high of chickenwire? In Europe that translate as about 90 cm (3 feet). I hope you have a roof on your enclosure, because adult rabbits can sure jump that high (and so can foxes)!

I'm hesitating giving you advise about the climbers:
You're looking for something that the rabbits would leave alone but that would not poison them? Or are you looking to provide them with extra munchies, planting on the outside and letting them nibble off the excess? I think they might quickly kill off most vegetation.
Is your fence pretty sturdy? Can it take some weight?

Texas may be too dry for these, but here in Tampa, Florida I would try muscadine grapes.  I know that the leaves of these are edible by humans, so they might even feed your bunnies a bit.

When I had some rabbits  years ago we kept them in a pen about 3 feet high with no top.  I can attest to them being able to clear that, so we enclosed the whole thing.  Even then they still got out, they're crafty little buggers!  No more rabbits for me...

sunchokes are a favorite of my bunnies, they arent a vine but grow fairly thick and I imagine the droppings would help them grow. I will be planting the tubers for us to eat and the rabbits eat the rest.

not sure how it would work in TX but I love woodbine vines here..they cover very quickly..edible you could use grapes and the bunnies could eat them