The nightingale in question is not a bird at all. Throughout the canon of folk song the 'hear the nightingale sing' metaphor is aeuphemism for sexual activity, in the same way that 'Cuckoo's nest' is a euphemistic metaphor for the site of such activity. This is just a song about two young people sowing their wild oats, as is 'they both sat down together there to hear the nightingale sing.'
   I find it really amusing that generations of maiden school ma'ms encouraged their children to sing this song imagining it referred to a rural idyll. Thr song was called the Coprnish nighjtingale not because sex is specific to cornwall ( though incest might be,....well, North Devon too)but because it was a Cornish variant of the song.