Dogtrousers
Kilometre nibbler
There once was a man from Nantucket,"……………..
you lot can fill in the rest.
I remember one that begins that way, and doesn't have the obvious rhyme. He kept all his money in a bucket and had a daughter called Nan. It ended "And as for the bucket, Nan took it".
Off to google.
Edit. Here you go:
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.
https://en.wikipedia.org/wiki/There_once_was_a_man_from_Nantucket