The Godzone Dictionary: Of Favourite New Zealand Words and Phrases (2006) says:
The expression right as something has been used in English since medieval times, using a string of comparatives, such as trivet or ninepence. Right as rain emerged in the 19th century and took precedence over all the other forms, possibly because of its pleasing alliteration, and also possibly because rain is perceived as good, and causes growth.
But a book review of the 1955 Dictionary of Early English by Joseph T. Shipley in the June-July 1956 edition of The Crisis magazine says:
Few of us are aware that many commonly used words once had meanings, in many cases, quite the opposite as those now current. Right, in the phrase "as right as rain," originally meant straight in direction.
And The Wordsworth Dictionary of Idioms (1993) agrees. It says as right as rain is:
A pun on the original meaning of right = straight.
The Free Dictionary gives these meanings of right:
11. Straight; uncurved; direct: a right line.
2. In a straight line; directly: went right to school.
The American Heritage Dictionary of Idioms (1997) says:
In good order or good health, satisfactory, as in He was very ill, but he's right as rain now, or If she'd only worked on it another week everything would have been as right as rain. The allusion in this simile is unclear, but it originated in Britain, where rainy weather is a normal fact of life, and indeed W.L. Phelps wrote, "The expression 'right as rain' must have been invented by an Englishman." It was first recorded in 1894.
The OED's first quotation is:
1891 G. Parker in Good Words May 330 ‘Right as rain,’ said the engineers.
It appears in an earlier dictionary, A dictionary of slang, jargon & cant embracing English, American, and Anglo-Indian slang, pidgin English, tinker's jargon and other irregular phraseology (1890), by Albert Barrère:
Right as rain (popular), quite right, safe, comfortable.
There was six of us took the rattler at
King's Cross by the first train in the
morning, and we'd got three briefs and a
old 'un with the date sucked off— right as
rain we was ! We got a kerridge all to
ourselves, nice and comfortable. — Sporting
The earliest I found is in Hence these tears (1872) by J.B.L. Warren (read online):
" ... Is all quiet outside"? "Right as rain," replied Christopher, pushing his head beyond the door to listen.
It was also used in the 1870s in Australia and New Zealand. The earliest in the Australian Trove newspaper archive is from The Gundagai Times (Friday 25 August 1876 p2 Article):
this thoroughly practical farmer tells us he
has a crop of oats ten or eleven inches high,
looking as "right as rain," and he attributes
this result entirely to the fact of steeping and
manuring the seed, thus getting a start of the
And from New Zealand's Papers Past archive is the Akaroa Mail and Banks Peninsula Advertiser (28 January 1879, "The Sundowners Swag"):
I thought when the Bank business was played out that Knickers would be dead broke, but no, he is still to the fore, and "right as rain," for I heard him the other day stave off a long-suffering creditor by telling him "that that confounded Afghan war was the cause of his remittance not coming by the last mail."