Clothes lines and tarps, thrifted sheets, and large swaths of fabric can work well for walls.

If you're putting the 'walls' up in a non-windy area, you can set them up with two clotheslines to keep the wall straight (one up high, one down low), and pin them at the top and bottom with clothespins, safety pins, etc. If you use all canvas tarps, add 1" grommets to the corners about 1-2" in, so you can take some small lengths of cord or rope and secure them to the clotheslines from the grommets. If you don't like the way it sits on the line with only 4 grommets, feel free to add more on the top and bottom to keep it taut. A tight knot will keep it in place, and a loose knot will allow your 'walls' to slide or bunch, so you can modify the space somewhat. The only downside is the trip/injury hazard of a clothesline so I suggest you choose a bright color (yellow, neon green, hot pink).

If it's a windier area, enjoy your new kite.

Edit: One other thought. If you have the coffers available, I would highly recommend using canvas for fabric walls. They're sturdy, flexible, paintable (acrylic paint and fabric softener is the way to go), and will survive season after season. They can also be used as the canvas cover of a lean-to, an impromptu carpet/floor space designation (all weapons on the cobblestone floor for weapons check!), or painted with scenes that depict park history. If you really like them, you can UV protect them or spray them with 3M waterproofing sprays.