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That is, are counters (助数詞) an [open class of
words](https://en.wikipedia.org/wiki/Part_of_speech#Open_and_closed_classes)?

If yes: Is there an example of a counter that was added recently (say, post-
Taishō) and is now in current use by a community of speakers (i.e. not a
single writer)?

If no: When did new counters stop popping up in the historical record (that
is, when was the last period during which counter-words were an open class)?
There were precious few counter-words in Nara-period Old Japanese ( _-chi,
-ri, -ka,_ "pillar" _-hashira_ for gods), and there's an awful lot now;
therefore the class must have been open at some period. The standard
hypothesis seems to be that the Heian-era influx of Chinese influence expanded
usage of counters (by influence of Chinese classifiers/measure-words); but did
they stop adding counters soon after, or did they keep expanding the set up
until later periods?

For this question, I'm interested in grammatical counter-words like 個、匹、本、羽
etc. A counter-word doesn't just quantify general measures, as in "3 kilos of
flour/lettuce/uranium" or "3MB of data/bandwidth/free memory"; it's also bound
to specific sets of words, effectively dividing the lexicon into classes,
which it counts in natural units (small animals are counted as 匹, except
rabbits which are lumped with birds into 羽, while roundish objects are counted
as 個, etc.). Counter-words are also distinct from nouns like ダウンロード in
一万ダウンロード、 in that they can be used to count _different_ nouns in syntactically
[anaphoric](https://en.wikipedia.org/wiki/Anaphora_\(linguistics\))
constructions like:

  * ３ **個** の **りんご** を食べた。
  * **ポケモン** は3 **匹** ゲットした。
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history counters chinese language-change
Are Japanese counter words still being created?
Short answer: **still an open class, especially for Sino-Japanese _(kango_ )
and Western _(gairaigo)_ nouns, which can seamlessly be converted into
counters.** A “core” set is stable, but rarer, more specialized counters are
comparatively fluid.

I was overlooking a large number of _gairaigo_ borrowings used for counting,
some of them used as true grammatical counter-words (thanks @H. Ha for
pointing this). One important example is セット, when used (among other things)
for set meals or sets of products sold together. A few real examples from
Twitter:

  * > **定食2セット** くらい食べて欲しい

  * > みそ汁&ご飯も全てがパーフェクトなお味  
>  調子に乗って **定食2セット** 食べちゃった=3

  * > 一人で入ったのに、 **お冷やとおしぼり** を２ **セット** 出された(；・∀・)

(Detailed research on the uses and meaning of セット is available on
[東条佳奈、『名詞型助数詞の用法 :
準助数詞「セット」と「組」を中心に』](http://ir.library.osaka-u.ac.jp/dspace/bitstream/11094/51518/1/hnk27_109.pdf).)

Pamela Downing's _Numeral Classifier Systems: The Case of Japanese_ has more
information. Downing's research was motivated by two conflicting studies:

  * Sanches, _Language acquisition and language change: Japanese numeral classifiers_ , 1997, found that young people are using _fewer_ counter-words, implying that the system is on its way out in modern culture.
  * But 見坊 Kenbō , 現代の助数詞 (in: [辞書を作る](http://www.tamagawa-up.jp/book/b28317.html)), 1976 found exactly the opposite: that not only existing counters were being adapted for new uses (such as 面 for sports arenas), but also new ones were being devised.

After doing some detailed research on the functions of counters, Downing ends
up cautiously siding with Kenbō, criticizing some of Sanches' methods. As
shown by the discussion in the comments above, counter-words are surprisingly
tricky to define, and are closely related to common nouns. What's more, many
counters are infrequent, and catch on to varying levels of acceptability and
prescription (as shown by the popularity of 数え方 “how to count” manuals and the
like). Because of that, Downing says the class is "permeable", and may at any
time recruit nouns to be used as counters. She says there's a "core set" of
counters that are very frequent and stable in Japanese, and cross-
linguistically frequent in other classifier languages (that is, if a language
has counter-words, it probably features this set); the core includes counters
for generic inanimate objects ( _tsu_ ) distinct from people (人 _nin_ ), the
basic shapes (本、枚、個), and, secondarily, perhaps the most important
"kind"-based classifiers (台、匹…）. To this basic set, any noun may be added as a
counter, depending on cultural considerations.

Kenbō says that native ( _yamato-kotoba_ ) counters have been stable from the
20th century (at least?); but new Sino-Japanese ( _kango_ ) and Western (
_gairaigo_ ) counters are still being added. (Sadly, Downing's report is
lacking on concrete examples; if anyone has access to Kenbō, or some _kango_
examples, it would be appreciated).
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answer