I like to add large jump rings so the riveted stone hangs nicely on a chain.
Make jump rings by wrapping heavy gauged sterling wire around a steel rod. Use a jeweler's saw to cut rings. Always open jump rings with a twisting motion, never by pulling them apart, which will get the circle out of alignment. Sand the ends of the jump ring smooth. Fit one ring on to each riveted stone and twist back into alignment. Sand smooth and solder closed. Sand, oxidize and polish as desired. Now add a chain or hang from ear wires and you are ready to wear your little reminder of the beach.