Although they cover only a tiny fraction (less than 0.2%) of the ocean's bottom, coral reefs capture about half of all the calcium flowing into the ocean every year, fixing it into calcium carbonate rock at very high rates. Coral reefs release carbon dioxide to the atmosphere due to the chemistry of calcium carbonate precipitation. The release of carbon dioxide from coral reefs is very small (probably less than 100 million tons of carbon per year) relative to emissions due to fossil fuel combustion (about 5.7 billion tons of carbon per year).
Coral reefs store very little organic carbon and are not very effective "sinks" for carbon dioxide from the atmosphere. Forests are more effective sinks for atmospheric carbon because they convert carbon dioxide into long-lived structures: trees.