The first thing that came to mind was to make a Christmas tree skirt without the Christmas designs. The patterns come in all sizes, with different edges.
I went into a fancy store, checked out the sorta "fan shaped" place mats like ones I saw on a round table, went home and made a set. Corners can be squared off or rounded...which ever one is more comfortable for you to make.
Why not try and make a pattern that exactly fits your table. Make an L shaped piece of cardboard, the short arm an inch thick, the long arm the distance you want your placemat to be from the edge of the table (an inch or so) + 1 inch. Put a piece of paper on your table, draw a line with the aid of your L (short arm down along the edge) and as long as you want your placemat to be. Same thing for the top edge. The curve will be perfect this way. Hope this makes sense.