Confederate Jasmine would be a good choice (or any of the Jasmines - they are green year around). The only way this vine is invasive is if the vines rest on the ground. If you keep them trimmed, they won't do so.

Thank you.

Recommend the Clematis armandi, as I find it is beautiful until the last of Winter, and even then it looks presentable. Beautiful, and beautifully fragrant vanilla scented brief bloom in Spring.