Not an historian, but a physician who runs a podcast on medical history, and I recently did an episode on this question (in particular, what degree did scientific advances in medical knowledge of smallpox lead to its potential use as a biological weapon in the new world). There is one undisputed episode of smallpox being used as a weapon, and that's during the so-called French and Indian Wars in 1763, during the siege of Fort Pitt. General Jeffrey Amherst wrote to the local commander Henry Bouquet in a correspondence that still exists. “Could it not be contrived to send the smallpox among the disaffected tribes of the Indians? We must on this occasion use every strategem in our power to reduce them.” Bouquet responded, “I will try to inoculate them with some blankets that may fall in their hands, and take care not to get the disease myself.”
Given the timing of these letters, it's unclear that Amhert's orders were actually received by the fort. However, we have the diary of William Trent, a trader who wrote that at the close of a parley with Indian representatives at Fort Pitt the Indians asked for, 'a little Provisions and Liquor, to carry us Home', and that, 'we gave them two Blankets and an Handkerchief out of the Small Pox Hospital. I hope it will have the desired effect'. And then, later in the spring and summer of 1763, there was a smallpox outbreak in the vicinity of Fort Pitt, allowing the siege to be broken.
There's one other episode with strong circumstantial evidence, and that's of the smallpox outbreak at Botany Bay in 1789, where the First Fleet of convicts, seamen, soldiers, and settlers landed near the area that's now Sydney. There have been several competing theories on the origin of the smallpox outbreak, though it's now mostly accepted that it started with the British settlers. Complicating this is that it's quite unlikely that there was endemic smallpox among the settlers on the ships (the long journey was beyond incubation, and the settlers were investigated for signs of smallpox by the Surgeon General of the fleet). The fleet also had variolous material (dried scabs on satin ribbons) to use for potential variolation if they encountered smallpox. I should mention that by the middle of the 18th century, variolation -- the cutaneous introduction of smallpox into the skin by means of a cut, which produced a fair less severe disease and also conferred immunity -- had become the standard of care, and by the late 18th century the government had started to plan for variolation of the entire population, though vaccination would make this unnecessary. There have been several theories that given their desperate situation, the British may have purposefully used their variolous material to infect the aborigines. However, there is no documentation, though the idea was contemporaneous, with the captain of the Sirius writing, "It is true, that our surgeons had brought out variolous matter in bottles; but to infer that it was produced from this cause were a supposition so wild as to be unworthy of consideration.” In his letter, he clearly placed the blame on French explorers nearby.
As far as I know, there are no other convincing accounts of intentional smallpox spread (the claims that the US Army spread smallpox among the Mandans by Ward Churchill have been widely debunked).
Ultimately, to the best of our current knowledge, it appears that the spread of smallpox among indigenous peoples in the areas of the Inca and Aztec empires was likely unintentional. There is strong evidence that the British did intentionally use smallpox as a weapon in North America, and circumstantial evidence that they did in Australia. This is unsurprising, as the British had far and away the most experience in preventing the disease, having embraced variolation on a population level, and would have had supplies of smallpox material throughout their colonies, as well as physicians comfortable using the disease.
Sources for this:
There's always room for discussion, but perhaps the section Disease in the Americas from our FAQ will answer your inquiry.