Rapidly Paint Fabric Flags?
Rollers in various widths with a fast drying acrylic. 

I would insert a piece of card inside each pillow to stop the design running through to the other side and to keep the fabric straight. Your challenge is to keep the fabric flat.

To speed the drying process, or to store or display finished or unclaimed works, rather than using a table, find some sort of rack arrangement, or use the sides of the marquee with bulldog clips. 

A hair dryer will speed up the drying process.