I don’t know if this is actually a folk song, but I found it mentioned in The Ballad Index at Fresno State University.

This political poem, which apparently evolved into a song, concerns a proposal to abolish the provincial governments of New Zealand. (They were actually abolished in 1876. See Wikipedia.)

From The Press , Vol. 18, Issue 2578, (Christchurch, New Zealand: Friday, August 4, 1871), page 3, column 7:

PROVINCIAL COUNCILS.

TO THE EDITOR OF THE PRESS.

Sir.—

There follows a commentary on the political issues of the day, followed by:

For the following lines I have no excuse to offer, save that they are apropos to the subject in hand, and can only trust that your readers will not be too critically disposed:—

John Bull of New Zealand is canny and keen,
And no one knows better what two and two mean,
But exceptions, they tell us, are proofs of a rule,
So in proof of the Sage we must show up the fool.

Does John ever look to the state of his till,
With eight little Senates to run up his bill?
Does John never think that the work might be done
By eight little Senates rolled into one?

Eight little Parliaments, sitting in state,
Eight little Speakers, and Ministers eight,
All sit but to show they need never have sat,
And the country grows lean, as officials grow fat.

Has John ever heard of the froggie who died
Of a great deal of wind in his little inside?
How he puff’d himself up, till his poor little skin
Was bound to let out what he’d just taken in?

Let Johnny take warning before it’s too late:
One rat in the larder is better than eight,
And Councils Provincial are dear at the rate,
If John, like the froggie, must die to be great.

Yours, &c.,
S. B.
Opawa, August 3rd, 1871.

- - -
On November 18, 1872, the Timaru Herald contained an article:

GERALDINE ELECTION.

CAPTAIN BULLOCK AT TEMUKA.

On Friday last, Captain Stanley Bullock addressed the electors of the provincial district of Geraldine at the Crown Hotel Assembly Rooms, Temuka. About 100 persons were present….

After a long account of his speech, the article continues:

He would with their permission read some lines he had written on the subject, and which had been published in the Press newspaper. He did not mean that he held precisely those views now, but he still considered that the Provincial Council was open to improvement.… Captain Bullock then read the following lines:—

and the poem is repeated.

The poem was reprinted in several other New Zealand newspapers:

Evening Star [of Auckland, indexed as Auckland Star], 30 November 1872, presents the poem with this introductory paragraph:

The following lines were recently recited in an election speech down South:—

North Otago Times, 24 December 1872, presents the poem only, with no discussion, titled PROVINCIALISM, attributed to “Press.”

Marlborough Press, 15 January 1873, presents the poem, with no title, but with the introductory paragraph:

The following lines, which will be generally appreciated, were delivered by Captain Bullock at a recent election:—

Evening Star [of Dunedin], 25 January 1873, presents the poem, with the same introductory paragraph, under the title EIGHT LITTLE PARLIAMENTS.

West Coast Times, 8 February 1873, simply reprints the Dunedin Evening Star article verbatim.

All of these may be seen at https://paperspast.natlib.govt.nz/

The poem/song is said to be included in

Rona Bailey & Herbert Roth, editors, Shanties by the Way: A Selection of New Zealand Popular Songs and Ballads (Christchurch: Whitcome and Tombs, 1967), page 32, under the title ABOLITION OF THE PROVINCES.