Seconding what Osewme said about the flannel backed table cloths, also look for them and/or things designed to cover gas grills or patio furniture at places like Big Lots or Home Goods. Even if isn't quite the right shape, I'd think there would be some yardage in something designed to cover a high end outdoor living room chaise lounge.
There is a wide variety of quality among flannel backed table cloths... if you don't care about the cutesy or timeliness factors you can pick up some quality after pretty much every holiday season on sale.
There are things you have to keep in mind for water-protective seams. There are ways to fold/construct them. Things to use to seal them. Other things to do. I'm here in the Seattle area, I can tell you water has many tricks and I've learned some ways to get around them too. Sometimes what you think is decorative piping is really functional and there just to deflect the water way from the seam line.