Answer: You might find that a rhododendron would do well in that location, but this is a relatively slow growing shrub. Most vines would prefer at least a half day of sun or more, so this may not be the ideal solution either. Instead, you might consider a small understory tree such as the native redbud, or perhaps create an etagere of shade tolerant potted flowering plants on that "wall" of the deck. Another solution would be to hang trailing foliage plants such as English ivy along with some annuals such as impatiens for color. Yet another solution could be to hang an attractive drape or canopy on that side. I hope this gives you some ideas; I would also caution you that it is possible that the area is sunnier than you are expecting, since the sun angle changes between winter and summer.
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