In looking up an old video short from (I think) the 1980s called The Cat Came Back I found that it was based on a song from the 19th century, but the original title was, The Cat Came Back: A Nigger Absurdity. I googled the phrase and it shows up in a number of titles of what appear to be short plays or songs, possibly from vaudeville or similar formats? Does anyone know the history of this term and what kind of performances it was a part of? Was it exclusively American?
(An expert on American musicology and/or Vaudeville would be able to speak with more authority than I and for the same reason--my amateur level knowledge in this response--there's more reliance on wikipedia research in this response than I'd like... My history-of-blacks-in-American-culture class was like 8 years ago and I have no idea what texts we used.)
The song was a slightly sneakier than normal Coon Song, the musical incarnation of blackface comedy. The composer, Harry S. Miller, had many songs like that and used stereotypically "negroid" dialect, exaggerating Black Vernacular. The original first verse of The Cat Came Back:
"Dar was ole Mister Johnson, he had troubles ob his own // He had an ole yaller cat that couldn't leave its home. // He tried eb'ry thing he knew to keep de cat away // Eben sent it to de preacher, an' he tole it for to stay."
seems to imply that the narrator is a Southern black telling the story of how the members of his community fail to get rid of a cat 9 times (often causing disaster in their failure) until in the final verse an organ grinder wanders by and, on hearing him play, the cat spontaneously keels over dead. We can pretty much discard the "seems" thanks to the "Nigger Absurdity" subtitle.
It looks like there are very few works that name themselves exactly that way, but the larger "humor about the inferiority of blacks" genera was marketed with many on-the-nose names like "Black Face Plays", "Ethiopian Farces", and "Ethiopian Dramas". Generally, like "The Cat Came Back", they rely on the comical incompetence of black characters to reinforce the idea of White Superiority... Their character and popularity followed those of Minstrel Shows. The racist viciousness of their humor waxed and waned from the 1830s to the 1930s from exhibitions for people legitimately interested in black culture, sometimes even featuring "genuine negro performers" instead of blackfaced whites, to mere humorous stereotypes sometimes showing blacks as cleverer than their masters (though of course for that to be humorous there has to be an initial buy-in to the idea that they should normally be inferior), to pseudo-scientific phrenological analysis like in The Darkey Phrenologist, which also went by "Nigger Absurdity" proving the "inherent criminality of the negroid race".
I'm not sure how popular these things were internationally; a lot of content relied on Americans' emotions regarding slavery and segregation but there's lingering international interest in strange places for "darky iconography".
Mod note: Marked NSFW, in the future we prefer if you keep slurs out of the title (although it's fine to use them in their historical context such as this in the body of the text of course) just because people browse at work and our font is rather large.
FWIW, I've found one reference from Australia in an early 20th century newspaper, so I guess it's not a purely American phrase (if it's an American phrase at all...). To quote:
The concluding piece was a nigger absurdity, which caused roars of laughter, and the audience would not be satisfied till the performers re appeared.[1]