I was thinking it maybe related to the hardship times in the US but that does not make sense. The coin that mlov posted is a 2 sen dated 1877. The other two coins in tokencatalog are 1/2 sen which is worth just a quarter of a 2 sen. I cannot make out the character that are countermarked on the 1/2 sen. For argument sake they circulated around the same time, I would be surprised that they are worth the same. Were all these coins found in the US? If so, the only logical thing that I can think of is that this could be part of the large Japanese influx to California back in 1870s. Perhaps used in Japan town back in the days?
Wow. Yet another possibility. And very believable. I had one of these I sold and I still have this one. Both were same date, same denomination. I bought these in the USA, yes.
Here is a far-out explanation for the two sen coin: "The Two-Sen Copper Coin" is a Japanese mystery story written by Hirai Taro under the name Edogawa Rampo in 1923. It is considered the first Japanese mystery story and is one of the most well-known pieces of detective fiction of the period. Hirai Taro was a fan of Edgar Allan Poe's writing and hence the name "Edogawa Rampo". Japan 2 Sen Meiji 10 (1877) Bronze, 32 mm, 14.26 gm