A very hot torch with a very small tip may do it but pearls, shell, coral and many stones just can't take the heat.
Mechanical joining with rivets is usually done cold with tools that "peen" over the end of the rivet. Watch maker staking tools might be useful and often show up on the used market.
You might search the Ganoksin Orchid forum for words like "rivit" or post your questions there. Orchid is a forum with a lot of very innovative crafts jewelers and practicing gold and silversmiths. http://www.ganoksin.com/orchid/orchid.htm
Those of us in this forum will be glad to answer where we can but I've only done cold heading on rivets like you describe. Dee has melted ball heads on wire to use but only before beads or pearls were put on.