The Japanese 1 yen is dated Showa 32 (=1957 AD). The Thai 1 baht has a date in the Buddhist calendar and written in Thai numerals, but I can't read it in your photo. If you can get a better (more in-focus) photo of that coin, I may be able to figure it out.
For the Japanese coin, the date appears on the reverse bottom, underneath the "1," with the characters 昭和三十二年, read left to right and pronounced roughly "Show-wa san juu knee nen." Here is a more detailed breakdown: 昭和 = "Show-wa" this is another name for the Emperor Hirohito 三 = "San" or three 十 = "Juu" or ten - Three before ten, three times ten, or 三十, equals thirty 二 = "Knee" or two - add 2 to 30, or 三十二 to get 32. 年 = "Nen" or "year" - this designates the preceding number as a year All put together, the date reads "The 32nd year of Showa" or the 32nd year of the reign of Emperor Hirohito, which someone else already pointed out corresponds to the year 1957. That particular series of 1 Yen coins, made of aluminum and capable of floating in water (but don't try this unless you want to damage the coin), began in 1955. It looks like you have a pretty nice early example of this coin, though this series doesn't generally carry much value.