Sounds like you know Manx and probably a lot of songs, but it struck me that what you had was similar to "The song of the travelling fairies" or "Arrane ny sheeaghyn troailtagh".

It is a lullaby with hushing in it and it the version an an OAK publication of "Folksongs of Britain and Ireland" includes falcon, blackbird, wren etc. It could be a variant of that.