There's so many Nanny/Nancy songs it's difficultto speculate,isn't it? I quite fancy a Nanny-O quoted by cahppell as being in the Roxburghe Collection.

It is Nanny Nanny Nanny O
The love i bear to Nanny O
All the world shall never know
The love I bear for Nanny-O

The tune for that got around a bit as a fiddle tune at the right sort of time. Admittedly it's nanny not nancy but that's a minor difference.