Mike,
Put the old pinstripe down where you want the line. Then put down blue painter's tape or green frog tape (I like the frog tape better) on either side of the pinstripe tape. Peel off the pinstripe tape and press the inside edges of the blue painter's tape or frog tape firmly down and then paint the vacant stripe with the paint pen.
Shouldn't have any bleed through, although street and parking lines aren't perfect anyway.
You may have to wait until the first one dries completely before doing the next one, depending on your line spacing.
