I have done reading in the past about the history of Native Americans in the past, and from what I have learned I think it qualifies as a genocide. The actions of all the major colonizing powers, England, France, Spain, and Portugal (along with the United States and successor countries) actions constitute at the very least ethnic cleansing. In 2000 the Head of the BIA came out and used those very words to describe the actions of his agency in a public apology for the history on this continent. http://www.tahtonka.com/apology.html I also can find evidence of Native Americans being sold into slavery in California and North Carolina: http://nahc.ca.gov/califindian.html and www.gilderlehrman.org/history-by-era/origins-slavery/essays/indian-slavery-americas
While it is not in the United States, the extent of brutality expanded as far as downright hunting in Tierra del Fuego of the Selknam people. https://en.wikipedia.org/wiki/Selknam_Genocide
The actions of the colonial powers against the Native Americans at times were in response to Natives stealing the goods of the colonizing powers. The reaction unfortunately frequently became collective punishment against the entire group. This further emphasizes the overuse of military against Native Americans. The Navajo Wars started when a single Navajo man stole a horse from a white settler. In response to the actions of a single individual the American military massacred numerous Navajos. https://en.wikipedia.org/wiki/Navajo_Wars
Of course, the most famous case is Andrew Jackson's movement of the Cherokee to Oklahoma in the Trail of Tears. This forcible deportation which killed thousands of Cherokee on par with other genocides definitely qualifies.
Raphael Lemkin invented the word genocide and defined it as thus: "Generally speaking, genocide does not necessarily mean the immediate destruction of a nation, except when accomplished by mass killings of all members of a nation. It is intended rather to signify a coordinated plan of different actions aiming at the destruction of essential foundations of the life of national groups, with the aim of annihilating the groups themselves. The objectives of such a plan would be the disintegration of the political and social institutions, of culture, language, national feelings, religion, and the economic existence of national groups, and the destruction of the personal security, liberty, health, dignity, and even the lives of the individuals belonging to such groups."
To be completely clear, this issue is far from settled. A massive proportion of Native Americans were killed as a result of disease. Some of this was intentional, but most of it wasn't. The movement of Europeans acting as vectors for smallpox and malaria into different areas of the Americas was possibly the most devastating part of what happened on this continent in the first 400 years or so after Europeans first settled in massive numbers. This case in history is extremely difficult to fully untangle in a way which leaves us with a clear answer, which is why the population estimates for the pre-Columbian era for the Americas vary extremely widely. Despite all of this, I think the actions which were taken on top of the transfer of malaria, smallpox and other diseases is still sufficient for a verdict of genocide.
Given how the assimilate, die, or be impoverished policies of all the governments of the Americas were all regarding the destruction of the institutions of Native Americans and they destroyed all of those rights which Lemkin outlines, it would a great insult to all Native Americans to call the actions of all the countries towards Native Americans as anything but genocide.