I think the cover for piping is best made from something cut on the bias for going around corners. It is not like binding a quilt where strips cut on the grain are OK.
I've used the same fabric as for the item, and cut strips diagonally on my cutting board with the rotary cutter then stitched them together into a long strip. Then put the cord inside and stitched it down, and then sewed it into the cushion cover (or whatever).