"funny comedy" is correct and usable in written English.
You could use it to describe a genre of film or stage performance, or even a television show. For example, "I love to watch funny comedies to make me laugh."
NOAH BAUMBACH is the master of uncomfortably funny comedy.
It's all a mystery in this darkly funny comedy.
Rumoured to have made a very funny comedy about Islamic suicide bombers.
ROLE MODELS Paul Rudd is mainly the straight man in this wan, sentimental, occasionally very funny comedy.
But it's also an extremely funny comedy that pushes Rogen's instinctive good nature to the limit.
In shows like "101 Humiliating Stories" she transformed painful personal moments into achingly funny comedy.
She is starring now in The Overnight, an awkwardly funny comedy-drama about a children's play-date that takes a weird and sexy turn when the two sets of parents embark upon a decidedly adult encounter.
At three acts and more than three hours, this blisteringly funny comedy-drama is among the more ambitious new American works to be seen on Broadway in recent seasons.
The journalist was also chewing qat, it turned out, and the ensuing production was a not-so-funny comedy of phone calls and wrong turns.
It's true that critics are more likely than your casual comedy-goer to prefer formally inventive or not-just-funny comedy.
In his review of "Detroit" in Chicago, Charles Isherwood wrote: "This scary-funny comedy speaks to the fractious, frightened American moment more perceptively than any play I've ever seen on a New York stage".
