There is no way to fasten it reliably to the rig without either building a frame underneath, or driving screws into the rig. Friction-fit foam will fly away in heavy winds. Suction cups will come off with time, and/or rubber will become brittle. Duct tape will turn into dust after one hot summer (and what will remain, will be a pain to clean off the rig).
If this is a permanent site - build a frame. Whatever you put on it, is not critical. Can be a block foam, can be plywood, can be discarded corrugated metal or fiberglass, pieces of siding, truck tarp - whatever you can get for cheap or free. Dissimilar pieces can be painted. Under the front you can put a piece of plywood on two hinges to make a shed for items not too valuable.