They are normally made with batting. The *biggest* thing is to avoid over-stuffing. I did that with the first puff quilt I made and it turned out so stiff no one (except, perhaps, for a dog or cat) would want to use it. It is much better to under-stuff. To that end, I think you are better off cutting batting to a uniform size for stuffing the puffs.
Edit: I also think this is a situation in which polyester batting, such as Hobbs PolyDown, may be a better choice than cotton batting.