I want to make ceramic wine stoppers, which glue would work best?

I want to make ceramic wine stoppers, like this, but I don't know what glue would work best for attaching cork to the bottom of the ceramic piece.

I would like to have the glue be non-toxic, since it would be near wine, and have it be water resistant. A website I visited said carpenter's glue is both non-toxic and water resistant. Would that work well with ceramics? Would another glue work better? The bottom of the ceramic piece is not glazed if that helps.