Honeysuckle. Lonicera Sempirivens: 'Major Wheeler', 'Alabama Crimson'.

Just avoid the Lonicera Japonica. Its very invasive!

I thought Honeysuckle was poisonous?

I think the only part that is toxic would be the berries, and they would have to be eaten in large quantity. A dog could only eat berries at the bottom few feet, and the birds would probably get most of them first.

There is a chance that it could happen.