That's a nice melody at the  Max Hunter Collection  that Bun pointed to:  

Problem is, Caroline has more than one tune associated with it.  There are two other versions in the database here:

Blooming Caroline of Edinburgh  A version from Sam Henry's Songs of the People, with midi of the tune.
Caroline of Edinburgh  An American version from The New Green Mountain Songster; with midi of the tune and another from Huntington's Songs the Whalemen Sang.

I'm guessing, though, that the tune you want is the one often called  Come All You Tramps and Hawkers.  There's a midi of that here:  Paddy West.

You can see staff notation for it at the  Digital Tradition Mirror Site:

Paddy West  Staff for the two DT versions of Caroline can be seen there, too.

Malcolm