Old world cuckoos are brood parasites, cowbirds are new world birds, so it is that cuckoos are longer established in culture as parasites: the cuckoo is a pretty bird... a nest she never buildeth, a vagrant she does roam. And if you know the British film Village of the Damned about the town where the women give birth to alien children, it's from a book called The Midwitch Cuckoos. So I would have known to go with cuckoo, although I do think cowbird should be acceptable. (FWIW American cuckoos are occasionally parasitic but not habitually. They also do not inhabit clocks.)