Historical reenactors use canvas "oil cloth" to keep things dry. Basically it's a cotton canvas that's painted with boiled linseed oil, lamp black, and Japan dryer.
The ones I've used are as good or better than vinyl tarps in most every way, the possible exception being weight.
Here's a link to recipes both historical and more modern. Hope it's of some use......
http://44tennessee.tripod.com/articles//oilcloth.pdf
