To get coral you should build the Coral Mining. You can find it in the third tab of the Store window (icon with a mallet in the lower part of the screen). Note that this building will be available to you only on high game levels and you will be able to construct it only on Ancestor's Atoll after completing relative quests.
In case you want to get this rare resource immediately, there is no necessity to wait for it so long: you can find coral in the last tab of the Store window.
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