Place the craft paper on the high chair seat. Draw the outline of the seat on the paper and cut it out for a template.
Pin the template on the oilcloth and cut out two pieces of cloth, adding 1/4 inch past the template edge.
Cut out four pieces of 12-inch-long nylon cording. Stack the oilcloth pieces on a flat surface, right sides of the fabric facing each other. Fold one piece of cording in half and place the fold under one corner of the fabric, 1 inch from the corner edge. Repeat with all the cording pieces on each corner of the fabric.
Pin the oilcloth edges in place. Sew a straight seam 1/4 inch from the edges around the seat cover, leaving a 6-inch opening.
Turn the cover to the right side and fill it with polyester fiberfill. Hand sew the opening closed. Tie the cords of the finished seat cover to the legs of the high chair.