"There is not much coffee."
This is not a negative form, although hopelessly seems like one.
少ない is an adjective meaning few, little.
Maybe it's not very natural to say There is little coffee? So it was translated to Not Much.
You can also negate it to express a fact not normally anticipated.
The number of Americans living in Tokyo is not small at all.
コーヒーは多くないです wasn't accepted. Doesn't seem like the が particule would be obligatory here like with 欲しい, so 多くない would be the problem I'm guessing, but why wouldn't it work here? From what I understand from Keith_APP's comment, 少ない is it's own word representing "little", rather than being the negative of "much", which is what Duo seems to want, i.e. 多くない, no?
Also, I feel like the 少ない kanji keeps smirking at me for getting the question wrong dang nabbit.