Well, please don't use English Ivy - that is such a pest plant! How about Clematis armandii?

Here is a link that might be useful: Clematis armandii

If you have ever seen the Carolina Jessamine sprawling along the tops of pine trees, then you know that they can readily cover your trellis. You will simply need to prune occasionally to keep it full on the bottom.

Thanks for the follow-ups. I searched for the Clematis Armandii, and I would have to wait until next spring to plant. (My local nurseries dont have any in stock). I might just go with my first instinct of the Carolina Jessamine...........ahh, then I wont have to wait either! Thanks! (I am open to any other suggestions!)

I have a confederate jasmine that climbs to the top of a huge old live oak and drips from every limb. It is in full bloom right now, and the fragrance is to die for.

Betty

There are several other choices that are available...

Silver Lace Vine comes to mind. And one I have growing is a climbing hydrangea (although it is deciduous). Another is the Sky Vine which is in the thunbergia family of vines. Coral Honeysuckle is another favorite.
You can find most of these in the Charleston area nurseries.

Akebia is another possibility--beautiful evergreen vine, very hearty and fast growing. In the spring, it has tiny purple flowers. It grows up columns at the Summit, an outdoor mall in Birmingham and is gorgeous!! I purchased a plant after seeing it at the Summit and have had it about three years and am very pleased with it. It also roots very easily. It is also called chocolate plant. You can go to Hortiplex at Garden Web and see pictures and read more about it.

Cross vine is pretty. Grows to 30 feet evergreen here in 8b and mine has bloomed all year. It has orangish trumpet shaped flowers and the hummers like it. Also it's a fast grower.

I love my winter jasmine. It puts on a lovely show in the winter when all else is cold and dreary.