The phrase anything for a quiet wife is a jocular variant of anything for a quiet life, a phrase expressing concession or resigned agreement, to ensure one is not disturbed.

The latter phrase is first recorded in the title and lyrics of a broadside ballad, Any thing for a quiet life, or, The Married mans bondage to a curst wife to the tune of Oh no, no, no, not yet, or, Ile neuer loue thee more (London: Printed by G. P., [ca. 1620]). In this ballad, a young man, presumably an apprentice, is forced to obey the commands of his demanding master; he marries in search of “liberty” but finds his new wife just as demanding. The phrase occurs in the first line of the ballad and in the last line of each verse—the following are the first and last verses (source: Early English Books Online):

Any thing for a quiet life a Yong man faine would [missing word]:
To serue his Master out his time, and please his Mistris too:
His bondage wisht for liberty, that he might haue a wife
At his owne will, for to doe still any thing for a quiet life.
[…]
Let Yong-men all take heed by this, how they doe match and marry:
He leads a life of libertie, that doth the longest tarry.
It is the formost step to woe, to wed vnto a wife,
That will haue still, at her owne will, any thing for a quiet life.

The second-earliest occurrence of anything for a quiet life that I have found is from The sincere Convert, Discovering the Paucity of true Believers; And the great Difficultie of Saving Conversion (London: Printed by T. P. and M. S., 1643), by the English Puritan minister Thomas Sheppard (1605-1649):

The way of moderation or honest discretion, Rev. 3.16. which indeed is nothing but luke-warmenesse of the soule, and that is, when a man contrives and cuts out such a way to Heaven, as he may be hated of none, but please all, and so doe any thing for a quiet life, and so sleepe in a whole skin.

The phrase then occurs in Eikōn ē pistē. Or, the faithfull pourtraicture of a loyall subject, in vindication of Eikōn basilikē. Otherwise intituled, the pourtraicture of His Sacred Majestie, in his solitudes & sufferings. In answer to an insolent book, intituled Eikōn alēthinē: whereby occasion is taken, to handle all the controverted points relating to these times ([London:], Printed in the year, M.DC.XLIX. [1649]):

I think it good policy, any thing for a quiet life.

The English naturalist and theologian John Ray (1627-1705) recorded the phrase in A Collection of English Proverbs Digested into a convenient Method for the speedy finding any one upon occasion; with Short Annotations. Whereunto are added Local Proverbs with their Explications, Old Proverbial Rhythmes, Less known or Exotick Proverbial Sentences, and Scottish Proverbs (Cambridge: Printed by John Hayes, Printer to the University, for W. Morden, 1678):

Any thing for a quiet life.

The author and lexicographer Guy Miège (bap. 1644 – d. in or after 1718) recorded and translated the phrase in The short French dictionary, in two parts. The I. English and French, [The] II. French and English; according to the present use, and modern orthography (Hague: Henry van Bulderen, 1701):

Any thing for a quiet life, j’achete le Repos à quelque prix que ce soit.
     translation:
Any thing for a quiet life, I buy repose whatever its price.

The phrase occurs in a poem published in Jackson’s Oxford Journal (Oxford, Oxfordshire, England) of Saturday 5^th May 1759:

A Hen-peck’d Cuckold, bully’d by his Wife,
Must wink at any Thing for a quiet Life.

The earliest occurrence of anything for a quiet wife that I have found is from Graphic Proverbial Philosophy, published in The Daily Graphic (New York City, N.Y.) of Thursday 30^th December 1875:

Strike with the iron pot.
Brag ’tis makes perfect.
To each saint his scandal.
Anything for a quiet wife.
While we give let us give.
’Tis good to be wary and wise.
One swallow does not make a bummer.
A contented mind is a continual beast.
It is an ill wind that blows two in a bush.
The devil is not so white as he is painted.
A whistling boy is father to a crowing man.
Always laugh at your own jokes; if you want anything well done do it yourself.
A cursing goose never rolls to the mill for moss for the gander; and yet it is true that a bird in the hand always stays home to roost. Ponder this.