Do you think coral atolls disappear with rising sea levels? How then did they cope with previous dramatic sea level rises? See study below.?

No.  Corals can easily accommodate the sea level rise with growth.  Any warming tends to help corals build their reefs because calcium carbonate from which it is made is less soluble in warm water.  There is some compensation for that in increased carbonic acid making it slightly less alkaline but the increased CO2 helps corals with their primary food which is photosynthesis from their symbiotic algae they hold within their bodies.  The photosynthesis actually powers the removal of carbonates enabling them to grow even faster and easily keep up with any foreseeable sea level rise.   Sea levels, like climate, have never been stable.  Corals are very adaptable to varying conditions as are their zooanthallae symbionts.  

The headline is misleading.  Corals obviously won't drown.  If for example a coral broke off a shallow portion of the reef and landed in a deeper portion, it wouldn't necessarily die.  It would likely expel its zooanthallae and try they try to acquire different ones that were adapted to the new conditions.  

For one thing, Earth's temperature is rising much faster than it has for most of the past. As a result, sea level rise can be expected to rise much faster than it has in the past. And, in the past, when the temperature went up, oceans released carbon dioxide and became more alkaline. Since the current warming is due to carbon dioxide, this time oceans are absorbing carbon dioxide and the pH is dropping.

As sea levels rise, the reefs build upward. Besides, sea level rise has been slower in the past. It is "dramatic" only in geological terms, not historic ones.