Coral is very susceptible to higher levels of CO2 as demonstrated by scientists on a a group of 3 uninhabited volcanic outcrops in the North Pacific called the Maug Islands.
Scientists chose this island chain to study the consequences of rising ocean CO2 levels because of its varying levels of CO2 emissions in the surrounding waters which mimics present day CO2 levels as well as those predicted for several hundred years into the future. It also hasn’t been been negatively affected by humans in terms of overfishing, tourism and pollution.
These 3 islands have volcanic vents that release carbon dioxide. A 3 month study showed that when the volcanic vents were actively releasing CO2, the coral around the vents would die off and be replaced by CO2 loving algae. Higher CO2 levels are unsuitable for coral as it makes the water too acidic for them to properly grow their skeleton while algae appear to thrive in this environment. 1
When the vents slowed their CO2 emissions, the coral would come back and displace the algae. When the vents increased their emissions to levels predicted next century, the coral would only start growing at a distance from the vents, where the CO2 levels dropped significantly.
Extrapolate this information to cover the entire ocean, and it becomes apparent that rising carbon dioxide levels are detrimental to coral production and, in a century, we could see an ocean void of coral, but green with algae. Life would persevere, but would not be nearly as diverse.