A lot of corduroys are cotton, so it should take the dye very well, although you are probably going to still see remnants of the striping no matter what you do. You can try starting with a round of dye-remover, this will lighten the stripes, but it won't remove them completely. Also, dye remover really stresses the fibers, (imagine bleaching your hair and then re-dyeing it). RIT dyes that you get at most craft stores work well, follow the directions, use salt or vinegar as a mordant to make the dye set better, and if you want a dark color, use more than it calls for (although for such a small item, that won't be as much of a problem).

Good luck!