These two words appear related in that they both have to do with death. A coroner is a government official who determines the cause of death, and coronary disease is a common cause of death.
Coroner and coronary are related, but their surprising root is crown, having nothing to do with death. The source of both is Latin corona for "crown".
A coroner is an official of the government or "Crown", an office originally established in medieval England. In England, Canada, and other British Commonwealth countries the federal government is commonly referred to as "the Crown", representing the King or Queen of England as the ultimate authority. In Canada, land owned by the Canadian Federal government is still referred to as "Crown Land".
The "coronary" heart condition is more properly called Coronary Artery Disease (CAD) or Coronary Heart Disease (CHD). The word coronary here comes from the crown-like shape of the arteries encircling the heart. These coronary arteries supply the heart muscle with oxygenated blood. If the arteries become blocked or "occluded" by atherosclerotic plaque, the heart muscle tissue can die, a condition called myocardial infarction, and lead to cardiac arrest (a "heart attack"). It seems ironic that the heart which is full of blood that it pumps to the rest of the body depends on these small arteries to supply it's own vital oxygen - sort of like a gasoline tanker truck running out of fuel. Heart bypass surgery is a common procedure to replace these plugged coronary arteries with ones taken from elsewhere in the body. See the June 28, 2011 blog post on my Stay Healthy Naturally blog for natural alternatives to bypass surgery.
Source: A.Word.A.Day for August 15, 2011. If you haven't already subscribed to this delightful free email service, you can sign up at http://wordsmith.org/awad/