The scope of this question makes it difficult to answer. It might be better to think of European conquests and displacement of Native Americans not as one single monolithic genocide, and more like a series of discrete (but interconnected) events which included specific acts of genocide as well as disenfranchisement, discrimination, warfare, and oppression.

If you're looking specifically at genocide, you first have to define the term to decide which acts qualify. For example, the UN Convention on the Prevention and Punishment of the Crime of Genocide includes in its definition of Genocide:

Forcibly transferring children of the group to another group.

provided such actions are done

with intent to destroy, in whole or in part, a national, ethnical, racial or religious group

Under this definition, the US policy of forcing Native American children into boarding schools with the aim of assimilating them into Anglo-American culture might be considered a form of genocide. The children were often banned from speaking their native language at these institutions and indoctrinated in Western culture. Although I doubt few people today would intuitively recognize this as genocide, it was intentionally destructive to native culture. These policies, along with others designed to break up native community identity, did not end until around 1975 when US policy turned towards self-determination.

In terms of armed confrontations, battles and massacres occurred into the late 19th and early 20th centuries with the Wounded Knee Massacre (1890) and the Apache Wars (1849-1924). There was also the famous Wounded Knee incident in 1973: a sit-in protest which ended in an armed skirmish between the American Indian Movement and the US Marshals/FBI.

If we extend our definition of Native Americans to Latin America, violent conflicts continued well into the 20th century and even up to the present day. The Guatemalan Civil War of 1960-1996 included a genocide of native Maya people, and logging and mining companies in Western Brazil/Eastern Peru continue to clash with native peoples as they (frequently illegally) expand their operations into native territories.

In short, conflicts between native peoples and white settlers haven't really ended on a hemisphere-wide scale, although the dynamics of conflict continue to change. Within the US and Canada, large scale conflicts largely died out around the turn of the 20th century but the policies of appropriating native land and undermining native sovereignty continued long afterwards, with only occasional violence.

An argument could be made that elements of genocide were still at work in the 1970s. The federally funded Indian Health Service was performing involuntary sterilization on women at a number of reservations in the west. As this article describes it:

Unfortunately, eugenic birth control had been resuscitated as late as the 1970s through voluntary physician complicity with an immoral national eugenic policy.