The earliest published version appeared in 1902 in the Princeton Tiger:[1][2][3]

There once was a man from Nantucket
Who kept all his cash in a bucket.
But his daughter, named Nan,
Ran away with a man
And as for the bucket, Nantucket.

Other publications seized upon the "Nantucket" motif, spawning many sequels[4][5]

Among the most well known are:

But he followed the pair to Pawtucket,
The man and the girl with the bucket;
And he said to the man,
He was welcome to Nan,
But as for the bucket, Pawtucket.

Followed later by:

Then the pair followed Pa to Manhasset,
Where he still held the cash as an asset,
But Nan and the man
Stole the money and ran,
And as for the bucket, Manhasset.
http://en.wikipedia.org/wiki/There_once_was_a_man_from_Nantucket