The coins of the Chinese provinces didn't have a date as we understand it — as a period of time elapsed since a moment defined as a time zero. Such a time zero usually refers to an important event in this or that religion, or to a revolution: Christianity — the Nativity of Christ in AD 0, Islam — Muhammad's departure from Mecca to Medina in AD 622, Buddhism — the death of Buddha in 543 BC, etc. As far as the Chinese calendar is concerned, there is no time zero. It consists of cycles, each cycle lasting 60 years. This cycle is called the sexagenary cycle. The numeral «60» is noteworthy in the sense of the quantity of its divisors, they are as follows: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. Thus it is very simple to subdivide such a cycle into minor ones. Is this the only reason for choosing 60 as a cycle's length? I think another reason is that 60 years is approximately the length of a human being's life; people have always been defining measurement units comparable to their own bodies' parameters (foot, yard etc.) or parameters of something related to their regular needs (kilogram, meter, pound etc.).
Another name for the sexagenary cycle is the stem-branch cycle, since that chronological system is based on 2 counting types: a cycle of 10 Heavenly, or Celestial, Stems and a cycle of 12 Earthly Branches. Celestial Stems are represented by the 10 columns in the table, and the Earthly Branches are the 12 horizontal lines, or rows, of the table. Half of the combinations are not used, because they have different parity. Therefore, the cycle repeats every (10×12)/2 = 120 / 2 = 60 years. The 12 Earthly Branches are associated with the 12 signs of the Chinese zodiac (Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Sheep, Monkey, Rooster, Dog and Pig), and the Heavenly Stems pairwise are associated with the Five Elements (Wood, Fire, Earth, Metal and Water).
The year is specified by two Chinese characters in the Chinese calendar (see the table on the left), in the following order:
[Celestial Stem][Earthly Branch].
Keep in mind: at that time Chinese text was written and read from right to left. This rule is applicable to coins as well. The green numeral in the top of the cells indicates the ordinal number of this or that Gregorian year in a sexagenary cycle. When you place the mouse pointer over a cell with the necessary year of the Gregorian calendar, the appropriate top and left cells with Chinese characters are highlighted. The table covers the years from 1830 AD to 2069 AD — that is 60×4, or 240 years. If you click on a year-link, you'll see how the date's characters are written on a real coin. A quick search feature is also available: start typing the Gregorian year you're searching for, and as soon as you've typed the last (4th) digit of the year, it instantly becomes highlighted soft-red in the table.
Please remember that the beginning of the year in the Chinese cyclical calendar does not coincide with one in the Gregorian calendar; neither does it depend on any of the dates of the Gregorian calendar. To be more precise, the beginning of the Chinese New Year depends on the arrival of the new moon.
Examples of finding dates on Chinese coins (dates refer to the Chinese cyclical calendar)
There are some typical places on the old coins of Chinese provinces where the two characters of the date are specified. Let's start with the place near the coin's edge, at the center:
As specified above, the characters on the coins are read from right to left (#1: 癸, #2: 卯), and the date inscription can be interpreted as follows: «卯癸», this inscription corresponds to the year 1903 AD.
The next place for the characters of the date is: near the coin's edge, closer to the top:
The characters are: #1: 丙, #2: 午, and the inscription «午丙» can be therefore interpreted as 1906 AD.
Another place for the date is: near the coin's edge, on top of the coin, in line with the Chinese characters of the Emperor's name:
The inscription at the top of the coin should also be read from right to left; it says: «年未丁緒光», which means: «Kwang Hsu, year 1907». Kwang Hsu (also spelled as Kuang-hsü or Guangxu) was the last but one emperor of the Qing Dynasty. Kwang Hsu (1871–1908) formal reign lasted from 1875 to 1908 AD. On the orders of the Empress Dowager Cixi, who was Kwang Hsu's stepmother, Kwang Hsu was succeeded on the Qing's throne by his 2-year-old nephew, Puyi. Later on, from 1932 to 1945 AD, Puyi became the leader of the puppet state Manchukuo (currently this is a territory of Manchuria, North China; it was occupied by the Japanese until the end of the World War II).
Not only in Chinese empire…
Some coins of the first decades of the Republic of China were also dated in accordance with the sexagenary cyclic calendar. On top of that, Singapore also has a few commemorative coins that use the sexagenary cycle, says gxseries. He explains that the main reason for this is as follows: Singapore is a country that has a lot of Chinese people that emigrated a long time ago, so it's a kind of tribute to the memory of Chinese traditions.