A significant portion of your time in Coral Island will be spent chipping away at dirt, and every now and then you'll unearth a Gem. Sparkly and valuable, Gems are great additions to your inventory, and you should generally make space for one if you find it in the wild. There are three things you can do with Gems:
  • Donate them to the Museum
  • Sell them
  • Give them to townsfolk as presents - unlike a lot of gifts you find in the wild, Gems are generally well-appreciated
Despite the money you can rack up by tossing Gems in your Shipping Bin, you should always donate the first of a particular Gem type that you find to the Museum. Contributing Gems to the Museum will slowly raise your Town Rank, which will eventually unlock new items, livestock, and quests. Once you've donated the first of a Gem type to the Museum you can do what you like with any more you find.

There are two ways to acquire Gems:
  • Destroy gem rocks. Occasionally while exploring the Earth and Water Shafts of the Cavern you'll come across rocks with gems jutting out their sides. Cracking them open with your Pickaxe will yield a Gem.
  • Open Geodes. If you break up a normal rock while swinging your Pickaxe there's a chance it will drop a Geode of some kind. If you explore the Water Shaft in the Cavern you'll find additional types of Geodes that contain more valuable Gems. Take the Geodes you find to the Blacksmith and they will break the rocks open for $20, giving you the contents. You can also purchase Geodes from Ratih's Black Market, docked near the Lighthouse after 20:00 on Monday, Tuesday, and Thursday, but they're expensive.

Below is a listing of all the Gems found in Coral Island as of now. Each listing includes the kind of Geodes you need to break open to receive the Gem inside, as well as the sell price. There's a decent chance that this list will expand as more of the island is unveiled in future updates. 
  • Earth Geode - Break rocks - 35 C
  • Water Geode - Break rocks in the Water Shaft - 35 C
  • Mystery Geode - Break rocks in the Water Shaft - 35 C
  • Amber - Break gem rocks - 145 C
  • Amethyst - Break gem rocks - 145 C
  • Aquamarine - Water Geode, break gem rocks - 130 C
  • Azurite - Water Geode, Mystery Geode - 260 C
  • Beryl - Water Geode - 272 C
  • Black Opal - Earth Geode, Mystery Geode - 351 C
  • Blue Quartz - Water Geode - 195 C
  • Diamond - Water Geode - 407 C
  • Crystal - Water Geode - 130 C
  • Diorite - Earth Geode - 115 C
  • Emerald - Mystery Geode - 130 C
  • Fire Agate - Earth Geode - 115 C
  • Garnet - Unobtainable
  • Granite - Earth Geode - 115 C
  • Jasper - Earth Geode - 234 C
  • Labradorite - Break gem rocks - 324 C
  • Lepidolite - Earth Geode - 115 C
  • Marble - Earth Geode - 176 C
  • Moonstone - Water Geode - 195 C
  • Morganite - Earth Geode - 176 C
  • Onyx - Break gem rocks - 149 C
  • Peridot - Mystery Geode - 290 C
  • Pink Crystal - Earth Geode - 176 C
  • Pink Diamond - Mystery Geode - 653 C
  • Quartz - Water Geode - 130 C
  • Red Beryl - Mystery Geode - 527 C
  • Rhodonite - Mystery Geode - 149 C
  • Rose Quartz - Mystery Geode - 223 C
  • Ruby - Mystery Geode - 486 C
  • Topaz - Break gem rocks - 149 C
  • Variscite - Mystery Geode - 145 C