What is the difference in meaning in these three sentences?
it might be funny
it could be funny
it may be funny
The answer was partially touched on in this post.
All three phrases indicate that the source (the person who is speaking or writing the sentence) does not find the subject (it) very funny. The subtle differences between the three are all about tense (either present or future) and degree of confidence.
"Could" is the conditional mood of the verb "can" and "might" is the conditional mood of the verb "may". Therefore, both imply the necessity of a condition that is not present. The joke might/could be funny, if (it were rephrased, it were delivered differently, the matter weren't so tragic, etc.). The joke may well be funny and the conditions for it to be funny may well be present, but, perhaps, it is not funny not so much because of any missing conditions, but, for example, because I have no sense of humor or because I do not know the antecedent facts.
"Can" has to do with ability, "may" has to do with possibility. The joke could be funny if it refers to facts that could be considered humorous by some, but it just was not structured well enough to clearly present the underlying humor; it could be funny if it were rephrased. The joke might be funny to people that have a sick sense of humor, but, in my opinion, it is not funny at all.
There isn't any real discerning difference between the three modal verbs: might, could and may in the context of your question. All three express varying degrees of certainty, and a lot depends on the speaker's intonation or in the context of the situation.
I disagree with e.James that could denotes "high confidence" and might "low confidence". Depending on the situation and how it was said, possibly. I would say that could suggests that the speaker is slightly more certain that the film is funny, but without a real context I will never be certain.
Possibly may is becoming less common in some parts of the world and is considered almost quaint and too formal by many. Nowadays, people tend to say and write maybe when instead there should be two words. "It's maybe funny", or better still "Maybe it's funny", has a more colloquial ring to it, and looks more contemporary.