If you can affix something to the building itself, maybe you could set up a square of shade cloth? You could probably figure out something that easily fold away during the winter and cool or shady days. This is just an example of what I found when I googled "shade sail"

{{gwi:1257259}}

Perhaps some inexpensive bamboo blinds could be hung from the balcony above. I'm assuming that your deck is actually a balcony, so you have somewhere to hang them from.

My Garden Blog

I assume you're using taller, sun-tolerant plants to provide shade to other plants. A search for "shade cloth" in online greenhouse supply stores should get you a pretty cheap material that you can hang up on a frame.

Jim