I know of at least one case where the natives reached the conclusion that Christian missionaries brought disease upon them. In 1847, Marcus Whitman, a medical doctor and missionary, his wife Narcissa, and several other missionaries and workers were killed by Cayuse natives at their mission near what is now Walla Walla, Washington. The incident has come to be called the Whitman Massacre. The attack is thought to have been in response to a measles epidemic.

Whitman had been one of the first travelers on the Oregon Trail in 1835 when he and a fellow missionary explored the Blue Mountain and Palouse regions of eastern Washington in search of arable land and converts. Whitman returned the next year with his wife and a number of other missionaries, families and workers. They established the Waiilatpu Mission and began agricultural and construction work that year. They ministered to the people, treated injuries and sickness and built an impressive community over the next decade.

Whitman and other missionaries had a peaceful but tense relationship with the natives. The Cayuse had, by then, 30 years exposure to traders, trappers and explorers so Christianity and white culture was not a new or particularly threatening phenomena. But there was an uneasiness on the part of natives stemming in part from their suspicions that disease, particularly smallpox, was associated with white settlement. Also several disputes had occurred between the missionaries and the natives. Most of the disputes were about white land use and the compensation the Indians expected for it. Finally, there was also a good deal of unease on the part of the Cayuse brought about by the use of poison by Whitman to control predators and for other uses. It was reported that the Whitman mission workers poisoned meat to kill wolves and that meat fell into native hands and caused illness. There were other stories that Whitman was poisoning vegetables to dissuade natives from pilfering them.

So against this backdrop of suspicions about whites and plagues, tension over land use, and the general weirdness about poisoning critters and people while at the same time practicing medicine on those same people, things hit critical mass when a measles epidemic broke out among the Cayuse in 1846.

The measles epidemic was particularly virulent and hit the Cayuse quickly and hard killing 200 of the 500 local natives. The Whitmans were suspected. Several Cayuse chiefs decided to send a party of natives to the mission to test their idea that Whitman's activities were the cause of the measles epidemic. When all the members of the party sent to the mission died, the Cayuse attacked the mission and killed 11 people including Marcus Whitman and his wife Narcissa. They then took about 50 missionaries and their families hostage.

A year later a settlement was reached between Hudson Bay Company factors and the Cayuse for return of the remaining hostages (three died in captivity). Later, four Cayuse chiefs were tried, found guilty of the massacre, and hanged.

End note: The origin of the measles epidemic in the Palouse was actually Sutter's Fort, California. A party of natives including Walla Wallas and Cayuse were on a trading expedition to California when they inadvertantly carried the disease back to the Palouse. You can read about it here.

Nch'i-Wa'na "The Big River" Mid-Columbia Indians and Their Land. Eugene S. Hunn with James Selam and Family. 1990

Edit: I forgot to mention this earlier but I would be cautious about attributing a figure of 90 percent to disease alone. It is the particularly toxic mix of disease, enslavement, displacement, war and a barrage of other aspects of the colonization of the New World that caused the precipitous population declines. I don't think anyone can really put a firm number on the declines either.

I talk about this topic in this series of posts from a few years ago. Of particular relevance to you will be this paragraph:

Because the unnamed Wendat Patient Zero lived close to the Jesuits, the missionaries again were blamed for the disease. "They observed, with some basis in reason," Lalemant wrote, "that since our arrival in these lands, those who were nearest to us happened to be those most ruined by the diseases and that the towns that welcomed us now appeared utterly exterminated. [...]In a word, we were dreaded as the greatest sorcerers on earth. Wherein truly it must be acknowledged that these poor people are in some sense excusable. For it has happened very often, and has been remarked more than a hundred times, that where we were most welcome and baptized the greatest number of people was in fact where the greatest number died. Conversely, in the cabins to which we were denied entrance, though they were sometimes extremely sick, at the end of a few days one saw every person happily cured."

We already have some great answers on the modern-day US. In this earlier answer I’ve written about Aztec accounts from colonial Mexico of the plagues that wiped out around 90% of the population by the early 17th c.

I should note that the demographic catastrophe in Mesoamerica came not "only" through disease, but rather that the diseases' impact was strengthened through other factors such as forced labor, European military campaigns and forced resettlements; and so varied by region.

As I mention there, Aztec writers expressed articulately the horror those various, massive outbreaks produced. Plagues had broken out before but not on this scale and with these horrendous consequences. I've not come across explanation attempts by native authors so far, partly because this was an earlier time. In the 16th century, most European writers did not attempt explanations that we would consider scientific today either. The epidemics where put down too lots of reasons, including the supposed will of God, and to dietary differences between Europe and America.

So as I mention in my answer, Aztecs in the 16th and 17th century were very much aware that horrific diseases were killing them off in unprecedented numbers (compounded by colonial policies), destroying whole communities and central elements of their culture in the process. Search for reasons for these plagues was complicated at that time, for native people and Europeans both.

Since I've seen some speculation here on the impact of disease, I would also highly recommend this answer by /u/anthropology_nerd on North American native accounts by which covers disease spread in detail.