Battlestar Galactica and Caprica allow us a few hints for the time reference system over the course of a few episodes.  The units of measurement are about the same as today:  60 seconds to a minute, 60 minutes to an hour, 24 hours to the day.  There’s 7 days in the week and 52 weeks in a year, giving us a 365 day year. (This is pulled from Baltar’s monologue/whine-fest about the number of DNA tests he has to do in the first season.)  There are months mentioned, but never how many.

Days are named as they are in English — Sunday, Monday, and Wednesday are mentioned, so it would be safe, if you want to be a canon-thumper to use the days of the week as is.

Month names are gleaned mostly from set dressing — paperwork, newspapers, etc. Generally, they use the name of months with an “-ius” added to them.  Ianuarius, Februarius, Martius, Aprilus, Maius, Junius, Julius, Sextilis, Septembrius, Octobrius, Novembrius, Decembrius.  (Bolded names are seen in set dressing, others are taken from The Caprican website.)

The years seem to be based on the arrival of Galleon at the Twelve Colonies — 2000 years before the Exodus.  This is based on dating in Caprica which is frequently shown as xx:xx:xx (year, month day.)  There are other systems in the BSG series, but they appear to be, like stardates, a complete and total mess.  I would suggest using the YR01 (Year 1) system from Caprica, rather than trying to make sense of Galactica‘s dating.

To make it a bit more exotic, yet familiar enough to be grasped by the players you could use the Greek weekday names: (Monday to Sunday): Selenes, Areos, Hermiou, Dios, Aphrodytes, Kronou, Heliou.