Going by evidence found in the manga the year where everything happens is 1994. A calender at Ryoga's house has the date printed and clearly says 1994 (pictured above). The reason the calender is shown is because Ryoga is using a means of divination somewhat similar to numerology called rokuyo (more on this can be found at this site: ROKUYO – Lucky and Unlucky Days in Japan). There is other evidence of it being mid 90's for example: the Aloha virus was said to have contaminated the island according to a diary Ranma finds on July 23rd, 1990 and a ten yen coin dated Heisei year 6 shows up enlarged several times - Heisei year 6 = 1994.
There is on other major thing that points to it being 1994, in 1995 the legal marriage age changed, under the new laws Ranma would have to be at least 18 to marry Akane.