I'm going to say D1.6 for Structural Stainless Steel. AWS D1.6:2007 clause 5.6.1 says that the backing shall be the same material used in the WPS and must be removed unless permitted to remain in place by detail drawings, specs, or the engineer. This isn't a prequalified combination, so plan on doing a PQR to support your WPS.

I've always found these types of questions interesting in that, if there isn't a code imposed by the end user then there isn't a code applicable by necessity. Qualification and welding would then be determined by your own manual and program.
So my answer would be that if you have read your customers spec and there isn't a code imposed then there isn't one. If there is no spec then there isn't a code then either. It is not incumbant upon a fabricator to guess which code is applcable for any given project. This is info that should be provided by contract documents.