Word for "Trying to be funny in a serious situation"
This is a tall order: none of the words here really conveys the idea that somebody is trying to defuse a tense situation -- only that somebody is making light of serious.
A word not yet appearing among the answers is flippant. The criticism above applies equally to this word, but at least it carries the idea that the audience is getting annoyed by the defuser.
A person who makes light of a serious situation is called "facetious"