But here's a trick. It turns out humans are the outgroup in terms of fur coloration. That is to say, in us, black is a phenotypically dominant trait. This is not the case in most mammals, where it's actually recessive - you have to get a gene from both parents to have black fur. This possibly explains why it's a relatively rare trait, but certainly not why it's never been clearly documented. A quick search does not reveal that the mountain lion genome has been completely sequenced; however we do have extensive samples, and coat color genes should not be difficult to pick out based on our knowledge of other cats. So, now we can see if among our samples there are variants, especially ones similar to the melanistic gene in jaguars. Those melanistic genes, if they exist and dark coat color is recessive, must also be hiding in the genomes of tawny heterozygous cats. In fact, given population genetics, you should expect MORE tawny cats to have those genes than black ones! (Unless your claimed mechanism of melanism is that all black mountain lions have fallen Pepe Le Pew-style into black paint, and much to their chagrin have to constantly refuse the unwanted advances of hot-to-trot melanistic jaguars.)
Here's a mom jaguar and her cub. To really illustrate the recessiveness of melanism I should have posted two spotted jaguars with a black cub, but this is damn cute, so look at it anyway.
The strength of this approach is that once you detect a variant or especially a similar gene to the melanistic jaguar gene, you can put together male and female heterozygotes in captivity and wait for 25% of their offspring to be black, and there's your proof. On the other hand, if no such variant exists, based on the number of animals you've analyzed, we'll be able to say "If melanism exists, it's less than 1 in x cats". (Probably some people wouldn't be satisfied until every mountain lion is sequenced, and after that they'll find another reason to keep believing.) I expect we must have hundreds or even thousands of cats' DNA at this point. My suspicion is that there are no black mountain lions, but of course it would be more interesting if I were wrong.
As a reminder, I have a wager offer to anyone that wants to take it about my home state of Pennsylvania, where mountain lions were extirpated by the 1870s. To be blunt, most of the claims of mountain lions in PA are urban-myth-type photos which have been circulating for years and can be found on Snopes, or excitable people not used to seeing wildlife. That said, because there are no lions there now, does not mean there won't be lions there again soon, since the PA Appalachians offer outstanding mountain lion habitat. My prediction is that by 2025, lions will be re-established in the state, as documented by physical evidence of *TWO* separate non-sibling or parent-offspring-related animals. Physical evidence can be DNA-verified tissue, spoor or fur, or of course the animal itself. (This helps keep smartasses from bringing their own.) In the last few years, lions are verified in Indiana and now Connecticut.