This post will show all of the Japanese menko cards I have which I can not identify. This is intended to be a permanent post, updated as cards are added or subtracted.
The card on the right has a K on the player's hat and KS on his jersey. The back janken symbol is larger and not in a circle. There's an image of a baseball player with the katakana word "error" next to him; the math equation in the symbol is 3927+3. The kanji characters say Venus ("Kinsei"). The Kinsei Stars (KS) existed only 1947-48, before being acquired by Daiei and becoming the Daiei Stars.
The card on the right has a player wearing a hat with a "G", with the shirt text looking like "IN" in the middle. The back has the kanji for "Daiei", which first had a team in 1949, as mentioned above. They were the "Stars" until 1956, when they became the Unions for a season.The G on the hat could stand for "Gold" (the first character in Kinsei") which would then make his shirt most likely say "Kinsei". That is my best guess.
Assuming that the kanji on the front references the teams on the front, this most likely is a 1949 set. Daiei first had a team in 1949, and they could have used old artwork for "Kinsei"; additionally, the Hawks were the league champions in 1948.