To state the obvious, the US Federal Government has never been violently overthrown, nor has anyone ever seriously attempted to overthrow it. There have been a handful of overthrows or attempts to overthrow a state or local government. At least one such attempt ended up in the U.S. Supreme Court -- the Dorr Rebellion.
The Dorr Rebellion took place in Rhode Island in 1841-42. Unlike all other states, Rhode Island had never adopted a constitution, but continued to operate under its colonial charter. Under the charter, only (adult, male) landowners could vote. It was not a serious restriction at the time the charter was written because most inhabitants were farmers at the time, but as the state urbanized and industrialized and took in immigrant laborers, more and more inhabitants were excluded from the vote, until by the early 1840's no more than about 40% of all white men could vote. The led to a dominance by rural interests that was strengthened further because each town had a single representative, regardless of population. Clearly, the situation was an injustice, but the controlling interest in the state were (unsurprisingly) unwilling to change it an blocked all attempts. After attempts at reform through the system failed, reformers resorted to extra-legal measures. They called their own, extralegal constitutional convention, drafted a new constitution, and put it up for referendum, which it overwhelmingly passed (particularly among propertyless men who were denied the vote under the old charter). The reformers then called elections under the new, unofficial constitution and had a slate of candidates elected, led by "Governor" Thomas Dorr, while the limited voters under the old charter elected their own set of officials. Two rival sets of officials claimed office, but it was the Charterite candidates who held the actual levers of power. The Charter government declared martial law, called up the militia to suppress the rebellion and (since the militia mostly stood to gain under the new constitution and were therefore of dubious reliability) asked for federal intervention as authorized by the Constitution, Article IV, Section 4. President Tyler declined to intervene, not because he believed the rebellion to be lawful, but because he saw little danger of violence, but he did make clear that he might change his mind if he saw a real danger of violent rebellion. In fact, the Dorrites attempted to seize the Providence arsenal (even in those days, there were military weapons denied to civilians), but were defeated and scattered. The violent rebellion was over. Soon afterward, the state authorities got the message and prepared a new constitution that greatly expanded voting rights.
So what is one to make of the Dorr Rebellion? On the one hand, in many ways it seems made to order for insurrectionists. Clearly it was in response to genuine oppression and injustice which had proven itself impervious to lawful remedies. It was untainted by the pro-slavery elements and (mostly) untainted by the nastiness of racism that make so many Southern insurrections so distasteful. It was also successful in the sense that, although it did not violently overthrow the Rhode Island government or even seriously threaten it, it did serve as a wake-up call and persuaded the Charterite government to institute necessary reforms. On the other hand, it did not, after all, violently overthrow the government, as insurrectionists seem to favor. But another reason the Dorr Rebellion may not play a large part insurrectionist lore is that it ended up in the Supreme Court and resulted the decision of Luther v. Borden, not a very favorable decision to the insurrectionist cause.
Next: Luther v. Borden