Well, I guess it depends how you define "secret society", but there was the alleged Business Plot in 1933 that is probably worth reading up on.

Now, whether or not this plot was a giant hoax or not is up for debate, though many historians do believe some form of coup attempt may very well have been in at least the early stages of being plotted. As the linked wiki page above puts it - "most [historians] agree that some sort of "wild scheme" was contemplated and discussed."

The "Business Plot" is an interesting conspiracy to look into, because it was claimed to center around some rather powerful and wealthy American businessmen who allegedly were attempting to stage a coup d'etat to overthrow then-President Franklin Roosevelt.

According to testimony made before the US House of Representatives in 1934, these businessmen attempted to recruit some very powerful military men into the plot - including Marine Corps Major General Smedley Butler, who at the time was the highest ranking US Marine, and at the time of his death in 1940 was the most decorated Marine in U.S. history. Major General Butler was actually the man who came forward and really blew the lid off the supposed plot, alleging the existence of this massive political conspiracy, and claimed that he was approached by members of this group to help create a fascist veteran's organization and then use that military force to help overthrow the President and install a fascist government.

Very specifically, has any secret society from the time period bracketed by the founding of the country until the present day, ever hatched a (serious) coup?