What can I cover the floor with?

Maybe you can just make an aisle out of the flooring and a dance floor. That shouldn't be tooexpensive. If you are already in a barn, the dirt floors won't look out of place, so why not keep them for the rest of the space?

Sawdust?

Try putting down visquine down on the floor than put plannter all around.

Depending on the theme of the wedding simple plywood might work. then maybe something fancier if you have a dance floor. 3or 4 by 8 sheet of plywood less than $20 and you could resell on Craigs list.

What about those foamy type puzzle pieces they come in all different colors & sizes,& they probably have a sandy type color & you could hose them off & re-sell on ebay/craigslist??

There is companies that rent floors for events. It might work for you.

Mulch??

You said you cant do hay but what about straw. I know they are similar but I have major alergy flare up's with hay that I dont have with straw.