This information is specific to Louisiana and may or may not be applicable to your area.
Vines suitable for an arbor include: coral honeysuckle, Madame Galan trumpet creeper, lady banksia rose, Carolina jessamine, muscadine grape (white variety to avoid staining), moonvine, cypress vine, morning glory, sword bean, jack bean, passion vine, Confederate jasmine, malabar spinach, air potato, Rose of Montana, and Chinese and evergreen wisteria.