Crows (and ravens) have usually represented Death in old ballads and poetry. 'Twa Corbies' for example, a gruesome poem about two crows looking at a dead knight and contemplating the delicious feast he will make. It could be because they eat carrion, and are associated with corpses and mortality.

I don't think there is an old song about a crow on a cradle particularly. The first line, 'The sheep's in the meadow, the cow's in the corn' is from the nursery rhyme 'Little Boy Blue' (come blow up your horn)