Hay bins!

I did use a hay bin but my piggies just slept in it and would get dirty. So I found that if I use a bent a gird and zip tie it to a grid above, it works just as fine.

I also use a bent grid. When I put hay in a pile or container that they can climb into, all they do is pee and poop in it and end up wasting a lot of hay. But if you still want to use the Tupperware bin, I have a large Rubbermaid bin that I use to line their kitchen area. I found some thin cardboard from a box of some type and cut some long strips and bent it over the cover up the sharp edges. I used clear packing tape to secure it on the bottom. This was 6 months ago and the cardboard and packing tape are still in tact. The pigs can't chew on the tape the way that I have it either, plus it's always covered with Carefresh.

I just bought one of these;

(broken link removed)

It was cheap and hooks nicely on the cage and keeps it dry and clean. If you have multiple pigs I think it comes in a larger size also.