I like to use tissue paper like what comes with a new shirt.  I cut it to the dimensions of a tarp, typically 12 x 12.  Lay it or them over the object and tack it in place with Elmer's.  This will not look like shrink wrap nor should it.  When satisfied with the coverage paint it dark gray or grimy black.  

Remember, tarps were pretty stiff (heavy) and did not always conform to the shape of the object being covered.

Tarps were tied down with ropes, wire or even nailed to the car floor.

Mont Switzer