In our vedic scriptures Mars or Mangal which is the lord of the gem Red Coral is considered incompatible with Mercury lord of Emerald..Hence Red Coral and Emerald should not be worn together

First off most of the coral you see now is color enhanced now so as to bring about a deaper richer color.
Coral in the color red is an excellent stone for the feminine energies during the 7 day cycle to help ease this time period.
It is one of understanding and communication, an excellent stone to use with the root chakra and vibrates to the number 4.
In general coral of all color helps with communication of a past spiritual nature to bring about the reawakining of the present and connection to the past histories of the individual that is using this stone, so that the transfer of such knowledge is easily understood.
Horn Coral is also one of a red color and as its name implies looks like a horn, and some say a tooth. your choice. This one is better suited to the bringing forth of past knowledge to the present.
Both the red corals are good for protection and brings self-awareness to your own security in all matters related to the individual using this stone.

Red coral should be worn in gold either as a ring or pendent.

I wear both Red Coral and Emerald they are both very good and alot of positive things wil just start happening out of the blue.

is used for the planet mars which for someone with a negative acting mars can be a sense of emotional outburst and temper as mars is the planet of action and passion and such things can be exhibited by a misbehaving mars. depression can also be relieved by wearing red coral. more importantly it is good for raising the tempt of the individual. furthermore holding red coral can help alleviate colds and flus and increase recovery time. because mars rules surgery wearing a red coral can expedite the time of recovery after surgery. red coral is a nice stone and increases the attributes of mars. it will instill strength of purpose as well. of course wearing red coral increases mars energy and the negative energy of mars is  thinking of bombs, explosions (similar to emotional outbursts, tantrums, depression, repressed anger), arguments and wanting to fight, aggression, etc. so if you have these thought changes as a result of wearing mars then it is not appropiate for you at all. the most important thing when wearing a stone is to see the changes in thought processes. your thoughts should have an instantaneous change. some thought should come in that wasn't there. that is my experience. of course please share your experiences as well. the chart is a genetic blueprint of yourself created by the arrangement of the planets. by the exact configuration of these planets and the strength of these planets radiating at the time of your birth determines the unique blueprint. hence someone can have the same configuration but the planetary strengths were different at time of birth can produce different results in the personality and fate of the individual.

wearing red coral must be carefully analyzed after wearing to ensure that aggression and negative tempers etc. don't arise greater.  

please read all assocations with mars related to vedic astrology online there are plenty of resources available.