It keeps raining on my smoking, so I finally picked up a Chimney Cap:
It's a standard 3 inch Chimney Cap that I simply "adjusted" with my thumb, and now I can jam it in the top of my Oklahoma Joe Longhorn Exhaust Stack whenever I'm cooking in the rain to keep the rain out. This should work for most offset sideburners with a 3 inch Exhaust Stack - and larger sizes and different styles are also available right off the shelf.
Just flip open your exhaust valve plate all the way (as it should be positioned whenever you're cooking) and then note that on the side where the rivet/pin holds the swinging valve plate there will be some interference to the fit of the chimney cap. No worries, just push your thumb against the bottom edge of the chimney cap's sleeve until it will fit into the chimney with enough clearance for the rivet/pin. Basically the bottom edge of the tubing will be a circle with an indent on one side. Remember that you're just jamming this into the exhaust stack when it's raining and otherwise storing it until you need it, so it doesn't have to be perfect. You might be able to find one in stainless steel, but galvanized is cheaper and durable enough - and shouldn't be a hazard at the low temperature of the exhaust stack. Zinc galvanizing melts at 900 degrees F, and vaporizes at 1650 degrees F. I bought a galvanized one.
Hope this helps with smoking in the rain!