I would strongly suggest the following actions:
1) Go to DuPont's web site and get the MSDS (Material Safety Data Sheet). This will have some data that can help identify what their glue is made of. Send it to me if you have trouble understanding what it says. Also, they may have some info on what Corian or the glue is made of, which would help in selecting a substitute.
2) Failing number 1, cut several small samples and try different "glues" until you find one that works.
My best guess is that the actual Corian approved glue is an epoxy, because what I recall from seeing Corian machined is that glue joints are formed by leaving a gap between the two pieces and then filling it with the adhesive. Then sanding the joint smooth. For the DIYer, CA or solvent (Acetone or MEK - methyl ethyl ketone) may be a good choice. I would try these by getting the mating surfaces as smooth and flat as possible. Then "clamp" them together with masking tape, and allow the CA or solvent to wick into the joint by surface tension. This should leave a nearly invisible joint and require only a minimal amount of sanding to smooth it out.
Chris Tully