You might want to try talking with folks who do a lot of leatherwork - I suspect there are forums on-line,or possibly even leather shops/craft shops in your area that might have the information. I would suspect that many adhesives might stain the suede, or stiffen it.
(If I were going to do it my first choice would probably be the spray-on 3M craft adhesive. I've used that to re-attach fabric, leather, and plastic trim and coverings on MANY things with no problems. I always have a can of it around, "just in case." The one I have right now is 3M #77, but other manufacturers also make a similar product. 3M info.)