"The longest lived in both species was 2,740 years and 4,270 years, respectively. At more than 4,000 years old, the deep-water black coral is the oldest living skeletal-accreting marine organism known."But that is granting too much.
This coral doesn't have a birth certificate. There is no "Made in China (C) 731 BC" stamped on the bottom.
The only way to date it is by making measurements, and using assumptions about initial conditions and processes.
This particular study used carbon-14. A carbon atom usually weighs 12 (6 protons and 6 neutrons), but some have two extra neutrons. This carbon is chemically the same, but will eventually degrade into nitrogen. By measuring the amount of nitrogen in molecules which should have carbon (or substances with nitrogen contamination), and comparing it to the amount of carbon-14 remaining, then - assuming we know the starting ratio of carbon 14, and that nothing has caused the nitrogen to escape, or added nitrogen - you can determine the date.
Carbon-14 dating has already had some "adjustments" (called calibration) to its calendar. The amount of carbon-14 in the atmosphere is assumed to be constant, and similar to current levels. Of course this is not true, so there is a constant process of trying to figure out what the levels were in the past (which relies on other dating mechanisms...).