Neither Child nor Laws covered this one, though there are other (unrelated) songs involving nightingales which do turn up in Laws. This is number 371 in the Roud Folk Song Index, and has been found mostly in the west and south-west of England. There have been a number of discussions about this song here in the past, but people have sometimes failed to understand that not all songs which mention nightingales necessarily have anything at all to do with one another, so some confusion has often arisen. The onsite search engine will find you more references; try looking for word-clusters rather than a title, though.