I'm just taking a guess here, they are probably made from nylon. I've never seen cotton in an ordinary pannier (I realize there are exceptions). Many local fabric stores do sell nylon by the name of "flag cloth", and is all you realy need. Do not get the real thin stuff often called "ripstop" or "tafetta" (the thicker stuff may have ripstop grids as well). Make the patch as large as needed and add an extra inch so you can hem the edges. Use a zig zag stich and sew around the edge of the patch, then around the edge of the hole, then some more stiching just for the heck of it. For extra security use some shoe glue and coat both sides. Obviously a sewing machine will help. An iron on patch could work as long as you get a patch made for synthetic fabrics. Even then, securing the patch with sewing is a good thing. If you have a sewing machine or patience and a needle, why pay someone else to do it? Other sewing tips, use non-cotton upholstery thread and a needle made for sewing denim.
Scott