Coral growth keeping up with sea level rise?
I have worked as a climate-change specialist in many countries including those with coral atolls, such as the Maldives, Solomon Islands and Samoa. I have analysed, at first hand, both the the tide-gauge and satellite-based rates of sea level rise. Notwithstanding the non-scientific writings of that well-known journalist, Andrew Bolt, the demonstrable truth is that ocean acidification is real and unstopable for the foreseeable future. The sea surface is warming faster than expected a decade ago, and the rate of sea level rise is accelerating. In the southwest Pacific, which is particularly prone to El Nino intensification, these affects are even more alarming. 

I point out that Bolt has zero scientific credentials, has never done any climate research, and is only able to make a living as a climate-skeptic writer because many Australians are, by nature, predisposed to enjoy 'contrary' arguments, irrespective of the science. 

Much research has gone into coral growth over the last decade, particularly in peri-Australian waters. Current findings are that, under optimum conditions, the fastest growing corals can indeed grow fast enough to keep up with the current rates of sea level rise. However, this cannot continue indefinitely. The reef is a total ecosystem, of fast and slow growing corals, bryozoa, etc., which has an aggregate rate of growth of less than the rise of sea level. Fast growing pioneering corals eventually collapse if left to continue growing ahead of the rest of the biome. Note also the phrase "under optimum conditions". As Jan Doggen rightly points out, sea-surface warming beyond the optimum thermo-tolerance, acidification, and water pollution are all serious stress factors. Between them one can say that, apart from deep-water corals, there is hardly a coral reef on the planet that isn't  suffering from sub-optimal growth conditions. 

There is another somewhat unexpected threat to corals: ordinary sun-cream from holidaymakers swimming near reefs. The common sun-cream component of oxy-benzone (present in most sun-creams) is toxic to corals at only about 60 parts per trillion. Globally, an estimated 10,000 tonnes of sun-screen ends up in the oceans, near corals, every year. This has a noticeable negative impact on the reef.

Taken altogether, this quadruple whammy bodes ill for the world's coral reefs. When the reefs die, and sea level rises there will be nothing to stop sub-tropical waves eroding the very land that some Pacific Islanders live on. Even islands with higher elevations still have fringing reefs. They are all in trouble, because sea level rise and higher erosion rates will force a retreat from the coast (hopefully planned), with massive social, environmental and economic disruption. So yes, they are absolutely justified in getting agitated about reef degradation!