Shanxi old postmark: town and date
Town

The city is "运城" ("運城" is its traditional Chinese writing). That is a well-known city in 山西.

Date

Year: 己酉 (1909, 1969, 2029, ..) 
Month: 二月 (2nd Month in Chinese Calendar, or February in Gregorian) 
Day: 廿四日 (24th)

My guess is that date is a Chinese Calendar date. Since you said it was around 1910, so the year should be 1909. Thus, 己酉年二月廿四日 was March 15, 1909. 

However, I am not familiar with history and their convention in those years, so I am not 100% sure if the date is in Chinese Calendar or Gregorian Calendar.

Note that if this is Chinese Calendar, 己酉 doesn't align exactly with the year of 1909. A Chinese year starts from the Chinese New Year (a.k.a Spring Festival) and ends before the next, which means the tail of 己酉 might be in 1910. However, since it is 二月 (second month), it should be still in 1909.