Bungee Cords and an Umbrella
Of course, this might not be a great idea in high wind. But for most small storms, with a couple bungee cords and a golf umbrella you can give your camera and passenger seat a little extra rain protection. This might add a minute or two to your setup/takedown time, but could be worth the effort (aside from the weird looks you'll get from people driving by).
Loop each bungee cord once around the umbrella, then stretch the cords around the doorframe. Then hook the cords together inside the car.
These bungee cords won't scratch your paint, and they're small enough that you can still close the car door on them.
You can get these mini-bungee cords at Lowes or Wal-Mart for about $2.