I saw this rig a couple of years ago. It was a picnic table, pole through the center, and a big "umbrella" on top.
The "umbrella" was actually a transmission transparent cloth that let the signals right through it. In other words, the dish is under the "umbrella" aimed upwards and the umbrella is actually attached to the dish edge and the lnb enclosure. If you are on your deck, and can put your pole through a picnic table, and then sew up some lightweight cloth in the shape of an umbrella maybe you could fake them out,
Maybe the cloth they sell in the hardware depot stores that blocks out some, but not all of the sun.
Maybe paint the dish a charcoal gray