Jeweller's Cement, for cementing pastes and marquisates
Epoxy (e.g. Araldite) or Cyanoacrylate (superglue) the is certainly permanent, but 'permanent' means that the jewellery cannot be repaired at a future date without destroying the stone and part of the item.
Jewellers Cement is a special 'soft' adhesive, it fixes stones quite firmly (they won't fall out!) but you can, at a later date, force them out, scrape away the remnants of the adhesive, and start again.
Clean the surfaces, apply with a fine point (a cocktail stick is perfect), allow 24 hours to fully dry.
It might damage some types of plastic. It probably won't. But don't take the risk, do not use it for plastics (e.g. cheap costume jewellery).