1 Samuel 13:1 is corrupted, so we don't need to assume that Saul's reing
lasted two years, neither that he was one year old when he became king of
Israel.
A tradition recorded at Acts 13:21 assigns 40 years for Saul's reign.
In my opinion, only the events in 1Sa 14:47, 48, 52 are two much for two
years.
In 1 Samuel 7:2 Saul is a young man, but when he died, his son Ish-bosheth,
who must have been younger than Johathan, was 40 years old (2 Sam 2:10).
Also, David became musician for the king and his armorbearer before
defeating Goliath; then he became a noted soldier and then he had to fly
from him and live in the desert for a certain period; after a lot of events,
he went to Gath and lived there for a year and 4 months (1 Sam 27:7).
Certainly, all of the events narrated in the chapters 13-31 are too many for
a few years period.
Also, in 1 Samuel 17, David is too young to be a soldier (vv. 28, 33, 42).
He must have been younger that 20 (Num 1:2, 3, 45). However, when Saul died
David was 30 (2 Sam 5:4).
So, 40 years fits well with the narration in 1 Samuel 13 to 31.
However, Acts 13:21 assigns 40 years to Saul and 40 years to David, when in
fact David was king for 40 1/2 years. If the Israelites used the same system
than the Mesopotamians, Saul must have been king for 39 1/2 years, and
David's first 6 months were attributed to Saul's reign.
So, going back to 1 Sam 7:2: "And it came to pass, from the day that the ark
abode in Kiriath-jearim, that the time was long; for it was twenty years:
and all the house of Israel lamented after Jehovah." I think the 20 years
were the period since the ark was carried to Kiriath-jearim until 'all the
house of Israel lamented after Jehovah' and were gathered to Mizpah.