The phrase the cup that cheers but not inebriates and its variants refer to tea as a drink which invigorates a person without causing drunkenness.

It is from The Winter Evening, the fourth book of The Task. A Poem, in six Books (1785), by the English poet and letter-writer William Cowper (1731-1800):

Now stir the fire, and close the shutters fast,
Let fall the curtains, wheel the sofa round,
And while the bubbling and loud-hissing urn
Throws up a steamy column, and the cups
That cheer but not inebriate, wait on each,
So let us welcome peaceful evening in.

Apparently, Cowper applied to tea an expression from The Medicinal Virtues of Tar Water Fully Explained (1744), by the Irish philosopher and Church of Ireland bishop of Cloyne George Berkeley (1685-1753):

The fermented Spirit of Wine or other Liquors produceth irregular Motions, and subsequent Depressions in the animal Spirits. Whereas the luminous Spirit lodged and detained in the native Balsam of Pines and Firs, is of a Nature so mild and benign, and proportioned to the human Constitution, as to warm without heating, to cheer but not inebriate, and to produce a calm and steddy Joy like the Effect of good News, without that sinking of Spirits which is a subsequent Effect of all fermented Cordials.

The earliest instance of the phrase that I have found is from Travels through part of the United States and Canada in 1818 and 1819 (Glasgow, 1823), by John Morison Duncan (1795?-1825); the following was written in New York City on Christmas Day 1818:

At a tea party last night. A tea party is a serious thing in this country, and some of those at which I have been present in New York and elsewhere, have been on a very large scale. In the modern houses the two principal apartments are on the first floor, and communicate by large folding doors, which on gala days throw wide their ample portals, converting the two apartments into one. At the largest party which I have seen, there were about thirty young ladies present, and more than as many gentlemen. Every sofa, chair and footstool, were occupied by the ladies, and little enough room some of them appeared to have after all. The gentlemen were obliged to be content with walking up and down, talking now with one lady, now with another. Tea was brought in by a couple of blacks, carrying large trays, one covered with cups, the other with cake. Slowly making the round, and retiring at intervals for additional supplies, the ladies were gradually gone over; and after much patience the gentlemen began to enjoy the beverage ‘which cheers but not inebriates;’ still walking about, or leaning against the wall, with the cup and saucer in their hand.

The phrase has sometimes been altered as the cup that cheers and inebriates to refer to alcohol. For example, The Oxford Times (Oxfordshire) of 9^th August 1879 published an article about the annual grand fête of the Ancient Order of Foresters, which contains the following:

On entering by the turnstile the ground set apart for the entertainment, the first thing that met the view was a huge tent for the sale of articles of that kind which “cheers but not inebriates.” This appeared to be largely patronised, Mr. Haverell, of the Angel Inn, being the purveyor. Further on was another tent in which was sold “the cup that cheers,” and inebriates too, if you think well to get enough of it. This temporary establishment also appeared to do a thriving trade, and was under the management of our townswoman, Mrs. Mitchell, of the Crown Inn.

The phrase has been shortened to the cup that cheers, and sometimes applied to coffee, as in this advertisement published in the Burnley Express and Burnley News (Lancashire) of 1^st March 1952, which plays on two meanings of cup:

The Cup that cheers

The English soccer cup is not yet to hand, but you can be sure of a cup of our Famous Pure Coffee to-day. It is freshly roasted and ground just when you order it, which is one of the secrets of good coffee.
Specially ground for the percolator or cup.

Tom Jones and Metcalfe Bros.
31-33, Market St., Burnley
Nelson, Padiham and Todmorden

 

A similar pun is found in an article published in the Courier and Advertiser (Dundee, Scotland) of 14^th March 1952:

Let’s hope it’s Cup that cheers

Scotland’s supporters will almost forgive and forget the dreary trail of six successive international defeats if the Calcutta Cup is wrested from England at Murrayfield tomorrow.