While it may be true that European contact in many ways had a deadly effect on Native Americans after 1500, A) It may be a stretch to call it genocide, since most was a kind of non-deliberate and oblique transfer of disease and B) Not all of these diseases may have come from Europe.

Though smallpox may have been the biggest European killer (with cholera, influenza, typhoid, typhus, plague, diphtheria, measles involved), it is also known that syphilis and some forms of Tuberculosis are indigenous to the New World and possibly went the other direction.

Then, there's the case of the Cocolitzli Epidemic in Mexico in the 1500s (here I refer to Wikipedia). There were approx. 22 million indigenous people when Cortez arrived in 1520, upon which 8 million died of smallpox. Next in 1545, 12-15 million died in the 1st Cocolitzli Epidemic, upon which 2 million died in the 1576 2nd Cocolitzli Epidemic. Cocolitzli is thought by modern epidemiologists to at least partially have been a native salmonella or arenavirus, brought upon by unusual drought cycles and rodents. Europeans may have been complicit by organizing Native Americans into closer contact, but that closer contact was on its way also before the Europeans arrived. I'm from a family of Veterinarians, diseases and carriers are certainly not confined to Europe. It is extremely tragic what happened to Native Americans, but may also be the pattern of humanity when 2 dissimilar groups come into contact (ie Neanderthals and Homo Sapiens also).