From -ember in September, November and December, the expression ember months denotes the final four months of the calendar year, i.e., September, October, November and December. This expression occasionally occurs in the singular, as ember month, denoting any one of these months.

The expression ember month(s) occurs, for example, in the column Les Vieux Temps, by Floyd Knott, published in Teche News (St. Martinville, Louisiana, USA) of Wednesday 6^th January 2010:

After enduring harsh heat and hard work in the fields, many rural families looked forward to the “ember” months of September, October, November, and December. During these months sharecroppers received payments for their crops, paid annual debts to the local grocery stores, prepared children for the beginning of school and looked forward to many holidays.
Ember months are the only ones that were not named for a god or an emperor. In addition to ember months, there are also unrelated ember days. Ember days were days when meat was forbidden (besides Fridays) before the revision of the Catholic Church’s calendar by Pope John XXIII in 1962. Ember comes from the Latin phrase quatuor tempora which means four times *. Ember days occur on Wednesdays, Fridays, and Saturday [sic]. For 2009 the ember days were on March 4, 6, and 7, after the first Sunday in Lent, on June 3, 5, and 6, after Pentecost, on Sept. 16, 18, and 19, after Holy Cross Day, and Dec. 16, 18, and 19 after the third Sunday of Advent.
September, the first ember month, has been the traditional beginning of the oyster season and once again the government has tried to impose restrictions on the consumption of raw oyster. For those not familiar with the “r” custom with oysters, our elders would only eat oysters during months with the letter “r” in it, although many cheated by pronouncing the eighth month Argust.
September is named from the Latin word septem which means seven, although it is the ninth month of the year. It was the seventh month of the year until the year 153 BC when the first month changed from March to January. Later the months of July and August were inserted into the calendar by Julius and Augustus Caesar, and the seventh month became the ninth month although it meant seven. The same thing occurred with October meaning eight, November meaning nine, and December from decade, meaning ten.
There are more holidays during the ember months than any other four month period of the year. It is also a period when crime is on the rise and there is an increase in highway accidents.

[* Although there may have been some folk-etymological influence of Medieval Latin quatuor tempora, the noun ember in ember days, first recorded around 1000, was probably ultimately derived from Old English ymbryne, period, revolution of time.]

The earliest occurrences of the expression ember month(s) that I have found are as follows, in chronological order—perhaps significantly, all the earliest American-English occurrences are from Pennsylvanian newspapers:

1-: From The Dundee Advertiser (Dundee, Angus, Scotland) of Tuesday 29^th September 1863:

Consumption of Oysters.—It takes from two to three years before the oyster is matured to a size at which it can be lawfully sold, but even then it is not fit for consumption, but should pass into the fattening beds. The oyster fishery of most consequence in Scotland is that of the Firth of Forth. The oyster beds there extend about twenty miles from the Island of Mucra to Cockenzie, and are dredged in from four to six fathoms water. The best are procured near Burntisland, on a bed belonging to the Earl of Morton. Equally good are those obtained on the rocky ground opposite Portobello and at Prestonpans. It has been computed that between two and three millions are dredged in the Forth during the season of eight months. The take is best, and the fish in finest flavour, during what are called the ember months. The season begins with September, and ends with the following April. The city of Edinburgh alone is said to consume daily, during the season, from seven to eight thousand oysters. London consumes five hundred millions of oysters annually.

2-: From the Reading Times and Dispatch (Reading, Pennsylvania, USA) of Monday 21^st August 1876:

LOCAL BREVITIES.

Are you registered?
A soaking rain is needed.
The dog days were severe.
Three weeks until the Fair.
[…]
Hayes and Wheeler will sweep the country.
We will soon enter upon the ’ember months.
Temperance pic-nics are the latest thing out.
[&c.]

3-: From the Lebanon Daily News (Lebanon, Pennsylvania, USA) of Wednesday 23^rd August 1876:

Splinters.

Cool nights.
Politeness costs nothing.
See that you are registered.
If you desire help—help yourself.
Chicken thieves are again about.
Court was well attended yesterday.
The ember months will soon begin.
[&c.]

4-: From Public Opinion (Chambersburg, Pennsylvania, USA) of Tuesday 29^th August 1876:

Local Melange.—

Katydids.
New Moon.
New applebutter.
Can what you can.
Rabbits are very plenty.
The blush is on the peach.
A grave man—The Sexton.
The cricket is now musical.
The berry crop has played out.
The ember months will soon begin.
[&c.]

5-: From the Harrisburg Daily Telegraph (Harrisburg, Pennsylvania, USA) of Saturday 1^st December 1877:

JOTTINGS.

Will it snow?
Get ready for Christmas.
December 1—the last of the ember months.
Plant your Christmas advertisement in the papers.
[&c.]

6-: From Public Opinion (Chambersburg, Pennsylvania, USA) of Tuesday 11^th December 1877:

Local Melange.—

Court again.
Christmas in two weeks.
Do not walk on the railroad.
This is the last of the ’ember months.
[&c.]

7-: From the Valley Sentinel (Carlisle, Pennsylvania, USA) of Friday 14^th December 1877:

LOCAL NEWS, &C.

Kid gloves are getting cheaper.
This is the last of the ’ember months.
Sectional festooning is a new freak of florists.
Whoever conquers indolence can conquer most things.
[&c.]

8-: From a review of the year 1877, published in the Stroud News, and Gloucestershire Advertiser (Stroud, Gloucestershire, England) of Friday 28^th December 1877—this unsigned review later appeared in several other British newspapers, for example in The Peterborough & Huntingdonshire Standard (Peterborough, Northamptonshire, England) of Saturday 29^th December 1877:

One or two facts with reference to the London Season, as illustrative of a gradual change in our social state, should be noticed. Though, as has been said, the regular season, that which comprises the months of June and July, fell far short of its normal splendours, there is no doubt that during the Ember month of the year London was much fuller than for a long period it has been. Similarly, though from mid-August to mid-September the town was sufficiently desolate, it began to fill again after the latter date with great rapidity. Thus we seem to have witnessed in the course of the past twelve months something like a gradual and equal distribution of the activity, trade, and excitement, which were formerly concentrated into two or three months, over the whole annual period.

9-: From one of the unconnected paragraphs making up the column City and County, published in The Manitowoc Pilot (Manitowoc, Wisconsin, USA) of Thursday 23^rd October 1879:

The beautiful October weather is the subject of general conversation. It is rarely that one of the ember months brings such continuous fine weather.