I don't know any concrete numbers for either game, but AFAIK both games were supposedly released only to book stores. For Circus Lido, you had to reserve at a book store/stationary store just to get the game. I'm not sure why this was, but the Circus Lido ads even pointed this out. This was before those places even sold video games. Supposedly, no game/toy stores in Japan carried these titles. It wasn't in regular circulation like the rest of the PC Engine games. I doubt the game even sold that many or was even on the shelves at book stores (ie reservation only). Now, fast forward 10 or so years and the availability of Circus Lido is next to zero. Because no one really ever heard of the game and people who knew about it probably never seen it or played it, BOOM! instantly rare. That's my best guess about Circus Lido.
Now for Akiyama Jin etc etc... It came out late in PCEs life, 94-95. Again, supposedly this game was only available in book stores. I don't think this game was even covered in PCE magazines. If it was, I don't remember seeing it. Anyway, Akiyama Jin is/was a famous person dealing with various educational TV shows, books, games, etc all geared toward children. Now, NHK published this game on PCE (they also did Niko Niko Pun, Taiheki, and others) and I guess they own the rights to Akiyama Jin stuff too. So anyway, the package comes with a book and a PCE CD. Supposedly this entire package was marketed as a book w/CD, rather than PCE game w/book. Again, as with Circus Lido, the game went unnoticed by PCE gamers and probably overlooked in the first place because it's some educational game for kids from what I understand. Now, fast forward again to today and now it's insanely rare because:
- it's based on the popular Akiyama Jin properties
- overlooked/unknown by everyone back in the day due to being only available in book stores
- an educational game targeted towards kids.
- the PCE was effectively dead in late '94-95 time frame.
- no one can find any now.
Obviously, this is my opinion of why these two games are considered stupidly rare. Luckily after amazon found a ton of Circus Lidos, the price for that game has remained steady at Y5200 or so (retail price). I heard that Akiyama Jin game was available at amazon for a short time, but wasn't able to confirm it. I'm guessing that there's a least a few thousand but I have no basis for that.