Chiefly used in Irish English and Australian English, the phrase on the pig’s back (also on the pig’s ear) means in a fortunate or prosperous state.

The phrase on the pig’s back is a loan translation from Irish ar mhuin na muice, meaning:
– literally: on the pig’s back;
– figuratively: in a fortunate or prosperous state.

The following is from A Dictionary of Hiberno-English: The Irish Use of English (Dublin: Gill & Macmillan Ltd, 2004), compiled and edited by Terence Patrick Dolan:

muc /mʌk/ n., a pig < Ir. ‘Muc i mála,’ a pig in a poke. ‘Muc ar mala,’ a scowl (lit. a pig on the brow). ‘Ar mhuin na muice,’ very well off, doing well (lit. on the pig’s back).
[…]
muin, in the phr. ‘ar mhuin na muice,’ see muc.

The earliest occurrences of the phrase on the pig’s back that I have found are as follows, in chronological order:

 

IN IRISH ENGLISH

 

1-: From The Constitution: Or, Cork Advertiser (Cork, County Cork, Ireland) of Thursday 30^th April 1829:

DARBY TO PAT.

Dear Pat—We’re all upon the pig’s back here, and no wonder, since the Sasinahs ¹ are put down, and our friends carried the day. […] I’m just going to the shebeen to drink success to the boys.

¹ Sasinah is a variant spelling of Sassenach, denoting an English person.

2-: From a parodic letter of congratulation to Prince Albert, purportedly written by the Irish nationalist leader and social reformer Daniel O’Connell (1775-1847), published in The Age (London, England) of Sunday 8^th December 1839:

Mon Prince—I larnt a taste of Frinch when I was a Jesuit at St. Omer’s, so will excuse the exordium of my epistle. By tunder and turf! but I am bursting like a maly tator out of my skin wid joy at the thoughts of you, my darlint, marrying the Queen Victoria, whom I, in my Milasian expressions of endearment, term “the Little Lady.” Och! by the living Jabers you have cut me out clear and clane of the sweet cratur! Bad look to you, my jewel, for that same. Sure ’twas myself, after berrying the moder of my childer, had every hope in the varsal world of marrying the Little Lady myself. God bless her! but, as second best, I wish you joy from the cockles of my heart, you divil of the world! Won’t there be a “gitting up stairs,” by the powers of Moll Doyle! The base, bloody, and brutal will be on the pig’s back, as we say in ould Ireland; or, as the Sassenachs say, they will ride the high horse! The Divil fly off wid the Tories, say I, and wid the stunted corporal for an outrider, say I! If they were in, faith, my boy, you would never be so; and even as it is, my darlint, people say it will prove an IMPOSSIBILITY to you yet. Niver mind! Grab the dust, my darlint, as I do this blessed morning, which is my Rint day. The beautiful pisantry are coming down with the stumpy; and the Propaganda are doing the thing lovely, praise be to Jasus. When you git the tin, my darlint, of coorse you will contribute to support the ould religion. If not, by the blazes above me it will be up the country wid you. You will give me the first invite, of coorse. En attendant, I am, yours to command,
Dan O’Connell.

3-: From Bell’s Life in London and Sporting Chronicle (London, England) of Sunday 7^th June 1840:

IRISH SPORTING CHARACTERS.—NO. 1.
WILLIAM QUIN, ESQ., OF LOLOGHER CASTLE, COUNTY TIPPERARY.

[…] Billy’s excellent dad (as hospitable a man as ever lived) always conceived that Billy would teach them the way to go in Ireland; and, although too shrewd a man not to include a college education in his son’s early attainments, yet, that finished, he remarked that having now learned enough, he may quit the inside of the book for the outside; and devote himself to “leather;” and certainly in breeches, boots, or on saddle trees, Master Billy very dutiously did his best to please him, and to make the deed true father to the wish. In Billy Quin’s early triumphs, all sorts of races may be included. No stage struck hero e’er donned a buskin with more delight than Billy lugged on the leathers, equally prepared for battle whether the victory was honoured by a cool hundred, or a country-made saddle, which (hung aloft from the inn door) had been an apple of discord and temptation for the preceding week. There were others just as deeply bitten by the bit as Billy, but, ere long, the natural genius of the youth soared (I should say mounted) above his struggling contemporaries; and the farmer who had Billy up, always gave a loud shout “in the regard of the triumph he ad ovur de Macks wid all dere kimeens, whim he got de Buy dat ud knock de patir nosthir out af them;” and, one lucky day, when “he ris out af thim ontirely, ontirely, in three hates,” put him, as we say in Ireland, upon the pig’s back as a “rael divarthir ovur de coorse.” But it was not in those “Guerilla warfares” that Master William became the A. 1. of the county, but in some real out-and-out forlorn hopes, which, although a young one, he went through with all the vigour of youth, but, at the same time, with the coolness of a veteran.

 

IN AUSTRALIAN ENGLISH

 

1-: From a correspondence from the Clarence District, in New South Wales, published in The Freeman’s Journal (Sydney, New South Wales) of Saturday 11^th May 1872:

In the Clarence district there are two principal gold fields, one distant about thirty-five miles and known as the Little River, and the other fifty-five miles from Grafton. […]
[…]
[…] There are about 300 men scattered over the Little River reefs. So far as I can glean, there seems not the slightest doubt but that the Little River reefs are rich and payable, and shares in many claims have been sold for something more than remunerative prices to my own knowledge. I am glad to say many of my countrymen are in a fair way of “raising the wind” ² at the Little River. As soon as they get machinery, they will be on the “pig’s back.”

² The phrase to raise the wind means to procure money or the necessary means for some end.

2-: From a correspondence from Condamine, in Queensland, published in The Brisbane Courier (Brisbane, Queensland) of Friday 20^th September 1872:

Taking things as they are at present, we are getting on comfortably enough in this quarter, and all we want to put us on the pig’s back is, to find a copper mine somewhere near at hand.

3-: From a correspondence from Tingha, in New South Wales, published in The Armidale Express, and New England General Advertiser (Armidale, New South Wales) of Friday 2^nd May 1879:

We are all anxious to hear whether the tenders have been accepted for our telegraph line. This, together with a mail coach from Armidale to Inverell once a week, via Tingha, will put us on the “pig’s back,” and we hope Tingha will, at all events, brighten up again.