It’s a century-old term, now rare, for a deceptive story or scheme, pranks, tricks or other irritating or foolish carryings-on. If it’s familiar to you, especially if you’re not native to its former US heartland, it may be because you are widely read in the works of P G Wodehouse. He used it a lot, and is credited with being the first person to commit it to print:
I’ll hang around for a while just in case friend Pilbeam starts any rannygazoo.
Bill the Conqueror, by P G Wodehouse, 1924.
Early in its existence, in the 1890s, it became a word of the moment, especially among Washington newspapermen, though it was then spelled rannikaboo or reinikaboo. A syndicated article that appeared in many American newspapers in early 1898 explained its allure for journalists:
“Reinikaboo” is entitled to a place in the next revision of the dictionaries. It has grown into the degree of usage which warrants formal recognition in the language. A reinikaboo is ... a statement of news out of all proportion and almost out of relation to the facts, and yet having a certain origin and shadowy foundation. ... In the classification of the Washington newspaper men there are fakes, reinikaboos, and real news.
Chicago Daily Tribune, 9 Jan. 1898.
As there’s more reinikaboo around today than there has ever been, you may feel the word deserves to be revived.
As to where it comes from, we have to admit almost total defeat. Jonathon Green suggests the first part may be from the dialect ranny, rash or giddy. We might guess that the second part of the rannikaboo form could derive from kaboom, but that imitative term became popular only in the 1940s. A connection to peekaboo seems unlikely. Its various forms may have developed out of whole cloth through a need to create an expressive epithet.