Search Google images for 1950's placemats to get a feel for what they looked like. Most were either paper or vinyl covered. Fabric ones were simply one fabric sewn around the edges. Quilting was almost non-existant in the 50's, especially for non-bed uses.
The mid-century modern period was known for clean, sleek lines along with easy to clean kitchens. Fabric and food just didn't fit that mold. I'd simply look for fabrics that invoke that period and use a very geometric pattern reminiscent of the 50's dish patterns. Good luck!