It depends on whether it is brush calligraphy or hard pen calligraphy.
For brush calligraphy, it can be written as follows:
Xin Chou Zhong Dong/Han Yue XX book
Brush calligraphy generally adopts the traditional format. There can be a down payment for the signature. Only the next paragraph is common, and the format is: time (generally not Gregorian calendar)+(%place)+author+(respect) book, such as "Xin Chou Xia Yue respects the book in Gufengtang XX". In traditional calligraphy, the date is marked by the year and the month by the lunar calendar, which is not specific to a certain day.
for hard-pen calligraphy, if it is horizontally arranged, it can be in the modern format: XXX book on December, 221. If it is vertical, it should also be in the traditional format.
nickname of month
the first month: Meng Chun, Yinyue, Jiayue, Shouyang, Xiannian, Early Spring, January, Duanyue, Kazuki Watanabe musician, Xiazheng, Guanyue and Xinzheng
February: Jianmao, Jiazhong, Liyue, Hanchun, Huachao, Midspring, Huayue and Apricot. Jiansi, Zhonglu, Zhu Ming, Zhengyang
May: Jianwu, Yanyue, Midday, Noon, Curtain Moon, Midsummer, Puyue, Depressed Steaming, Petty Punishment, Singing
June: Dusk Summer, The Last Month Of Summer, Lin Zhong, Summertime, Lotus Moon, Escape Moon and Jingyang < Chanting the moon
October: bright moon, spring, Meng Dong, early winter, Kun Yue, Ji Yue
November: mid-winter, Jian Zi, Jia Yue, Chang Yue, Fu Yue, Huang Zhong and Han Yue
December: late winter, Jian Chou, Yan Yue, twelfth month, Jia Ping.