Is it just roundup? Or does he not want you using any herbicides? You could use clethodim, as RGriz mentioned. I don't know if cleth will knock it out completely, but it should give you enough of a jump to get a plot going.
Everything is a chemical at the end of the day, even Vinegar AKA Acetic Acid. Roundup is a systemic herbicide. All the organic alternatives are just going to be defoliants, and won't truly kill plants.No herbicides, period. Organic, ok, chemical, no way.