I have always been interested in Irish mythology, especially Fionn Mac Cumhaill. I also like to write in journals. Is there a way of combining the two? In other words, say, for example, the life of Fionn Mac Cumhaill, but in diary or journal form. I also noticed that there are no dates in mythology. So how can I overcome this?
Ludi's comments are on the button. Every civilisation has it's own calendar. The calendar consists of the time passed since a significant event. 'Time' is measured by the number of occurrences of a recurring event.
Your time is measured as the number of times the Earth has revolved around the sun. However, it could be measure using any arbitrary method. Today's date could be stated as 1.800.452 - the number of time Old Faithful has erupted since Independence Day.
Examine some children's concept of time:
"We are going to Disneyland next Thursday."
"How many sleeps is that?"
- So, to answer your question. Create any concept of time you wish. Some fictional civilisations have a concept of time which has no anchor. Events occur in the 'now', in the 'before' or in the 'after'.
One of the most common forms of dating in the pre-Christian era was by regnal dating. That is, events were recorded as occurring in such and such a year in the reign of king X. (For that matter, Christian era dating is actually regnal dating based on the reign of Christ as king.) The use of regnal dating would seem completely appropriate to the material in this case.
As @Ludi mentions on a comment, the big question is the motivation for writing a journal of one's adventures.
Correct me if I'm wrong but Fionn Mac Cumhaill is a warrior who leads a group known as the Fianna. Their adventures (for lack of a better word) comprise the Fenian cycle which is supposedly written down by the poet Oisín, who happens to be Fionn's son.
Looking at the setting above, it seems to me that the writing of a chronicle would probably be the best way of uniting mythology and 'journal', since some chronicles detail events day by day, just like a journal. Of course that requires eventful days.
If the writer is Fionn's son (or an assistant commanded by him), the motivation would be to transmit the glory of his father / lineage. Moreover, although some chroniclers were dry and boring, there were also chroniclers that brought events to life almost cynematicaly (I'm thinking of the Portuguese Fernão Lopes, 14th century, whom I know best).
As for dates (sorry, I overlooked that question), I'd suggest going with months and days of the week. Avoid mentioning years altogether. It is easy to just reference that it was the time when King X ruled over Xland, or that something happened a decade after King Y's coronation / marriage / etc.