No. Stimulants, like caffeine, may well increase coritsol levels but it's a silly idea to suggest that 2-4 cups of black coffee a day makes you put on fat.
What IS true is that sellers of coffee like Starbucks, Costa etc don't sell that many plain old fashioned black coffee (and if they do they give it a fancy name). They DO, however, sell a LOT of variations on Lattes etc which contain a LOT of calories. Heck some of the special seasonal versions (xmas ones for example) can easily be 700+ calories. Even a plain black one with 2 sugars starts to add calories if you drink a lot.
Example, an ex GF of mine was consuming something like 11 teas and coffees a day. She asked me to suggest how to lose weight. I cut the amount in half and she dropped 4+ pounds in a month with no other changes. It'd have worked just as well if she'd had the same amount as before but swapped sugar for a sweetener.