It seems like ever since the movie Quigley Down Under every movie depicting buffalo hunters has to show them using Sharps rifles. As just mentioned, the Rolling Block rifles were as popular, and maybe used even more once most hunters switched to cartridge rifles in the 1870's.
And there's plenty of documentation for believing the hunters were indeed the largest impact on the near extinction of the buffalo. But there are also some hunters whose conscience finally changed their thinking, and they did much to bring back the buffalo from that point. One well known cattleman who had his ranch hands kill buffalo off his land so they wouldn't compete with his huge herds of cattle was Charles Goodnight. Goodnight and his partner Oliver Loving were the basis for Larry McMurtry's novel Lonesome Dove, and Goodnight had no use for buffalo most of his life. Fortunately his wife convinced him he was wrong and she directed their hands to bring in every bison calf they saw to the ranch house where she personally nursed and fed them to adulthood. The adult buffalo were so attached to Mrs. Goodnight that anytime she was outside her home they followed her around like the family dog! As the herd multiplied they were turned loose on the Goodnight ranch, and Goodnight allowed local Indian tribes to take some for their own use. He also allowed them to take some of his cattle as long as they didn't get too greedy.
The history of the buffalo in America was recently documented in a 3 part PBS mini series and extremely well done, with lots of written documentation used to support the history. Anyone who thinks disease, or nature did anything much to contribute to their demise needs only watch the series as it covers early years, to the great hunts, to the return of the buffalo better than anything I've ever read.