Here's how I set out stuffing for smaller sewing projects, like the monkeys:
This was one of those mega-containers of "Cheezy Balls" you can get at places like Sam's. This year my husband was one of the adults in charge of the kids' Sunday School Christmas pageant, and they chose to have the Wise Men bear three "modern" gifts - among them an XBox, a bicycle pump, and a large container of Cheezy Balls - it was pretty awesome :).
Anyway, I washed out the container, removed the label, and stuffed it full of stuffing. It eliminates the hassle of boxes or bags, especially since stuffing is a supply FACS teachers like to purchase in bulk. It's large and conveniently clear, so that kids can find it easily (you know how you can point directly at something and they still can't see it?), and I can easily notice when it needs to be refilled.