I think regular cavas waterproofer would work well, Of course you'd need to make sure you had some angle on the tarp when set up, (you couldn't have a big sag in the middle like you can get away with with silnylon) and I know from some research that high thread count sheets will work better. I've also heard to pre-wash them on boil to shrink good first, then do it.

I'm actually kind of looking at this because I may make myself an oilcloth tarp - Someone was giving me a pile of poop about modern materiels while I said it didn't matter, it was all about skills and staying minimalist, and they more or less dared me to do without.. I'm contemplating doing west coast trail with no nylon and no plastics - supa old school (I have most of the stuff I'd need to do this anyway)

So the alternative would be oilcloth style, basically, linseed oil, wax, and turpentine - but that will make it brown and wreck the tie die effect, so what I'd do is:

1) Some high thread count cotton sheets.
2) Wash on ultra boil hot
3) Tie Die, dry
4) Sew a seam, and grommets or loops
5) Good old canvas tent proof (Nikwax sells one for canvas)

As long as you don't set it up like a complete tyro, it'll keep you dry.