Cockamamie — something ridiculous, incredible or implausible — is an intrinsically funny word, but it’s truly incredible that word historians believe it’s a close relative of decal, a design prepared on special paper for transfer to another surface. (It is instead sometimes said to be Yiddish, but this turns out not to be the case.)
The original of both cockamamie and decal is the French décalcomanie, which was created in the early 1860s to refer to the craze for decorating objects with transfers (it combines décalquer, to transport a tracing, with manie, a mania or craze). The craze, and the word, soon transferred to Britain — it’s recorded in the magazine The Queen on 27 February 1864: “There are few employments for leisure hours which for the past eighteen months have proved either so fashionable or fascinating as decalcomanie”. It reached the United States around 1869 and — to judge from the number of newspaper references in that year — became as wildly popular as it had earlier in France and Britain. The word was quickly Anglicised as decalcomania and in the 1950s it became abbreviated to decal.
The link between decalcomania and cockamamie isn’t proved, but the evidence suggests strongly that children in New York City in the 1930s (or perhaps a decade earlier) converted the one into the other. There was a fashion for self-decoration at that period, using coloured transfers given away with candy and chewing gum. Shelly Winters wrote of cockamamie in The New York Times in 1956 that “This word, translated from the Brooklynese, is the authorized pronunciation of decalcomania. Anyone there who calls a cockamamie a decalcomania is stared at.”
Quite how the word changed sense to mean something incredible is least clear of all. An early sense was of something inferior or second-rate, which presumably referred to the poor quality of the cheap transfers. It might have been influenced by words such as cock-and-bull or poppycock. Anyone who adopted the craze for sticking transfers on oneself may have been regarded by adults or more serious-minded youngsters as silly — certainly the first sense was of a person who was ridiculous or crazy; the current sense came along a few years later.