Here are a couple of tests that you can do at home. Genuine coral is made of calcium carbonate, which will effervesce and dissolve in acid; so choose an inconspicuous part of the questionable coral and use a cotton swab with lemon juice to see if it causes that area to form tiny bubbles. (For those experienced, nitric acid can also be used.) If it does, then it is real coral.
To see if this coral is naturally colored or dyed, rub an inconspicuous area with a rag drenched in acetone. If it has been dyed, the color will eventually come off on the rag.
Genuine coral is quite rare due to overharvesting in the past. Most of the affordable coral on the jewelry maker's market today, including much of Wirejewwlry's coral beads and coral cabs, is 100% legal bamboo coral, and comes from the Philippines. This is a type of coral, not a type of bamboo! Bamboo coral's natural color is gray, which means that most of the red coral available today has been dyed. Note: natural/genuine coral does come in a rainbow of colors, blue and lavender being the rarest.
If you notice on this image of a sponge coral cabochon, you can actually see the tiny algae cells that form coral.
Answer contributed by Dale "Cougar" Armstrong