A 500-yen coin could be a possibility. The 500-yen denomination is often used in Japan for national commemoratives, as well as the 47 prefectures.
There will be two different 500 yen commemorative coins - currently under voting process. To see the photos, see here: https://soranews24.com/2019/06/19/j...pics-needs-your-help-picking-the-best-design/
Japan's commemoratives differ from US commemoratives in two very distinct ways: Japan seems to have the sense to not make too many commemoratives per year and their designs, even the lesser ones, are almost always stunning without exception. The US and Canadian mints could learn quite a lot from the Japanese Mint.
In response to the original question, I don't think I've ever seen a commemorative coin in general circulation here in Japan. All of the normal circulating coins have the same design in each denomination, unlike Australia where I come from... In Australia, there are many commemorative 50c, $1 and $2 coins, plus plenty of collector's commemorative coins.
One other point.... There is a new 500 yen commemorative coin, 30th anniversary of the enthronement of the previous Emperor (Heisei). It's Heisei year 31 (2019), the last year of his reign, since he has now abdicated last month. However, this 500 yen coin is for general circulation. I got one, but in a coin shop, not in general circulation. It's bimetallic, copper nickel centre, nickel brass towards the edges.
Commemorative coins do circulated in Japan but for some reason gets hoarded big time. I also thought they don't circulate until I got a 1975 commemorative Okinawa 100 yen coin in early 2000. Even the silver 1000 yen coin did circulate when it was released in 1964 but literally disappeared within the year. Same could be said for 2000 yen note - usage went down in a couple of years.
There's other reasons for the lack of 2000 yen notes. People here in Japan just never liked them. Plus no ticket machines or vending machines take them. The only time I see them is when Aussie friends bring them in, after changing money at banks. Seemingly, there are loads of 2000 yen notes in Aussie, and I suppose, other country's banks. I collect a few every time they bring them in.