The British-English phrase to rain stair rods and its variants mean to rain very heavily—synonym: to rain cats and dogs.
The noun stair rod designates any of a series of rods placed in the angles between the steps of a carpeted staircase, used to hold the carpet in position.
These are the earliest occurrences of the phrase to rain stair rods that I have found, in chronological order:
1-: From Cycling Notes and Gossip, by ‘Montagnard’, published in The Sporting Life (London, England) of Monday 29th January 1900:
The Automobile Club is arranging a 1,000 miles tour to start on April 23 and finish May 12, the route being roughly London, Bristol, Cheltenham, Birmingham, Manchester, Kendal, Carlisle, Edinburgh, Berwick, York, Sheffield, Northampton, and London. It is a big idea and will test and demonstrate the capabilities of the autocar, and it is stated that the club will welcome the co-operation of cyclists all along the route. Were I choosing a part of the route to see how the cars behaved I think I should go to Carlisle and see the cars through to Edinburgh. I came the reverse journey once on a tandem, and for forty-eight miles it rained “stair rods,” which may account for the impression I have that if the motors can successfully tackle that stretch of road they can do anything.
2-: From Cycledom, by ‘Pedal’, published in The Birkenhead News (Birkenhead, Cheshire, England) of Saturday 21st March 1903:
Saturday’s weather, with all the beauties of its stair-rod rain, made a very pleasant exception to the fine spell of weather we have enjoyed this winter. One gets utterly sick of continually carrying overalls in readiness for the rain which never comes, but Saturday changed all that, and even the biggest glutton for climate must have been satisfied.
3-: From the column Humber-Side Echoes, by ‘White Friar’, published in The Daily Mail (Hull, Yorkshire, England) of Tuesday 25th June 1907:
While I write these lines even, the sky goes black, and the air seems full of stair-rods. If there is much more rain I shall throw up journalism and go into the umbrella and mackintosh trade.
4-: From an account of the Scottish Reliability Trials, organised by the Western Section of the Scottish Automobile Club—account published in The Morning Post (London, England) of Friday 28th June 1907:
Unhappily, in the phrase of Mr. Harry J. Swindley 1, it “rained like stair-rods,” lakeland being reflected in every yard of the roadway by a series of minor puddles seemingly emulous of swelling to the vaster proportions of Grasmere, Thirlmere 2, and the like.
1 Harry John Swindley (circa 1861-1918) was a member of the Automobile Club of Great Britain and Ireland.
2 Grasmere and Thirlmere are two lakes of Lakeland, i.e., the Lake District, in Cumbria.
5-: From On the Wheel, by ‘Will-o’-th’-Wisp’, published in the Labour Leader: A Weekly Journal of Socialism, Trade Unionism, and Politics (London, England) of Friday 2nd August 1907:
I remember once being on tour on a certain famous triplet machine, and the first three days was simply a chapter of accidents; but how the riders’ ingenuity blossomed! The final catastrophe took place between Woodstock and Oxford. There was no shelter near, and it was raining stair rods. The front tyre had gone, and we wheeled into Oxford with the front wheel bandaged in pocket handkerchiefs and the rain running out of our boots.
6-: From an account of the Stewards’ Cup, run at Goodwood, Sussex—account published in The Daily Mirror (London, England) of Wednesday 28th July 1909:
The rain poured in torrents of the stair-rod pattern at this period, and the light was further obscured by a sea fret, carried up by the south-west wind from the Isle of Wight direction.
7-: From Cycling Notes, by J. Urry, published in the Birmingham Gazette and Express (Birmingham, Warwickshire, England) of Thursday 20th January 1910:
Duty took me Lichfield way on Saturday—may blessings shower on the men who laid that splendid wood pavement between the Tame bridge and Wylde Green—and if the ride out was bearable and even lively betimes, what shall be said of the return journey, when skirting the city and dodging the wigwams? It rained in torrents all the way out—came down like splintered stair-rods that splashed into molten silver as they struck—and till Tyburn on the return journey was reached it never tired in its pitiless pelting, the one great consolation being that there is nothing quite so pure to breathe as a rain-washed atmosphere.
8-: From Our Cycle Scouts, by ‘Will o’ th’ Wisp’, published in the Labour Leader: A Weekly Journal of Socialism, Trade Unionism, and Politics (London, England) of Friday 3rd March 1911:
The weather during the past week has been what our Scotch friends call “saft”; that is to say it has rained continuously for four days. It is rather difficult for a mere Sassenach to decide exactly where “saftness” begins or ends, but after careful consideration I have come to the conclusion that it extends from a mere drizzle of rain right up to the variety it is possible to lean on.
So soon, however, instead of holding one up, the rain—or whatever particular mixture is on tap—sweeps one off one’s feet, in fact, when it rains stair-rods, then the weather is coarse; it’s a coarse day, as distinguished from a mere “saft” day.
9-: From an account of the Chester Cup, run at Chester, Cheshire—account published in The Daily Mirror (London, England) of Thursday 4th May 1911:
The rain came down in stair-rod pattern as the fourteen competitors paraded, and the huge crowds watching the spectacle, usually so gay, from the ancient walls and other uncovered perches, had a bad time.
10-: From the Darlington and Stockton Times. Ripon and Richmond Chronicle (Darlington, County Durham, England) of Saturday 24th June 1911:
Thunderstorm at Yarm.—On Monday afternoon a severe storm passed over the town. The lightning flashed in quick succession, and the thunder was accompanied by a heavy fall of hailstones, the rain coming down like stair-rods. The surface water grates were soon unable to carry off the water, and consequently some parts were flooded. Fortunately no serious damage was done.