here we have a locale tarp it place that tarps thousands of tons of hay around the area for the big hay farmers. For a fee of course, but they always have torn older tarps they sell for cheap but are still in usable condition. Might look into to see if there is a place around your area that does the same. Thats about the cheapest way I can think of.
I always use hardware store tarps and pallets but the tarps tend to tear, leak, shred, and I have to buy new ones every summer. I have heard the ideal tarp is a vinyl billboard advertisement. I believe its heavy duty and sounds like they are the ideal hay tarp. I have yet to get one of my own. Try contacting some of the local sign/advertising companies in your area that have some old vinyl if you think that would work for you. Just an idea to think about. Good luck.