Paper or plastic?
Back when I rode diamond frame bikes I just stuffed a plastic grocery store bag under my Brooks saddles. If I got caught in the rain the bag went over the top of the saddle. Not as cool looking (or sounding) as an aardvark saddle cover but it's functional and the price is right.
I haven't figured out what I'm going to do for my recumbent seat if I get caught in the rain.