Write date and time using 文言?
Some disagreements with above. 

Though '七曜' did exist in Chinese philosophy and literature from the very beginning, it is almost certain that the practice of using '七曜' to notate the seven days of a week came from the western world via India around the Tang Dynasty.

In spite of this, it was not until the dawn of the Chinese dynasties that Chinese people did really start to get accustomed to the idea of having in their life 'weeks' made up of seven days as Christianity began its spread in China, and finally with the foundation of the Chinese Republic 'weeks' became official in Chinese people's life. In China, people use numbers (星期一, 二, ...)to mark different days of a week except Sunday (星期日). It's now the Japanese practice to use '七曜' (金曜日, 火曜日, ...)to name different days.

Thus it's hardly noticeable in ancient Chinese language to use any terms related to the concept of 'week'. Most of the time, it suffices to state the year and the date.

There are two common systems of counting the days in ancient China. One is the Regnal Year (年号), according to different emperors, together with a cardinal number, e.g. 顺治二年. Sometimes the regnal year was so much used and the regnal names for the years became even much more famous than the actual names of the emperors so people directly use the regnal names for the emperors. In fact when people talk about emperors of Qing Dynasty 康熙，乾隆，顺治... they are actually using their regnal names for the years as a substitute of their long and tricky foreign names ('foreign' in regard to Han People).

Another system is 干支 (Ganzhi), which is the combination of ten heavenly stems '天干' (甲、乙、丙、丁、戊、己、庚、辛、壬、癸) and twelve earthly branches '地支' (子、丑、寅、卯、辰、巳、午、未、申、酉、戌、亥). This system is cyclic with a period of sixty years. This system is still in use today.

Next is the date. Lunar years were used in ancient Chinese (they are still used widely today). In every month there're thirty or twenty-nine days called by 初一, 初二...初十, 十一...十九, 二十, 廿一...廿九, 三十. It was also common to use the phase of the moon to state which day it is in a month (朔，望，晦).

Some examples：

永和九年(ninth year of Yonghe)，岁在癸丑(Ganzhi)，暮春之初 (at the beginning of the late spring). ——王羲之 Wangxizhi 《兰亭序》

壬戌之秋 (the autumn of Renxu (Ganzhi)), 七月既望 (the seventh month, the day after the day of the full moon). ——苏轼 Sushi 《赤壁赋》

About the hour of the day, it is absolutely ambiguous in ancient Chinese. Most of the time people just talked about the position of the sun or moon, whether it was morning or noon or afternoon and that was enough.

More precisely, people would use twelve Digan (地支), which I mentioned above, to divide a day into twelve intervals, which are called '时辰'.

Also people use '五更' to mark the five '时辰' of the night from seven 
o'clock till five of the next morning, such as in the idiom '三更半夜' (around midnight).

So your sentence could be possibly translated as 
每至休沐，吾犹日出而兴. (Every rest day, I still wake up as the sun rises).