Are Japanese counter words still being created?

Question

That is, are counters (助数詞) an open class of words?

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 constructions like:

• ３個のりんごを食べた。
• ポケモンは3匹ゲットした。

Answer 1

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』.)

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), 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).