Timeline: Unified Kingdom Kings
Three kings ruled over all the children of Jacob in ancient times. Those kings were Saul, David and Solomon. The dates for the main periods in the rule of these men can be known. At the end of Solomon’s reign the kingdom was divided by civil war and remains divided to this day.
We are out to fill a chronological gap from the end of Judges to the time when Solomon began to build the temple.
1And it came to pass in the four hundred and eightieth year after the children of Israel were come out of the land of Egypt, in the fourth year of Solomon's reign over Israel, in the month Zif, which is the second month, that he began to build the house of the Lord.began…: Heb. built F. Kings 6:1 KJV
1In the four hundred and eightieth year after the Israelites had come out of Egypt, in the fourth year of Solomon's reign over Israel, in the month of Ziv, the second month, he began to build the temple of the LORD. F. Kings 6:1 NIV
The article Timeline: Judges established that year from Adam for that temple work was 9980 AA. That same article left off at 9907-07 AA, which we pick up here.
Unified Kingdom Kings
Three kings ruled over the entire family of the children of Jacob. Those kings were Saul, David and Solomon. This was the high point of the national power. This power and prestige ended at the civil war in the reign of Rehoboam.
The children of Jacob, in a way that is much like us today, refused to let God remain king over their land. They wanted a human king. One which would be like the kings they could see in the lands around them.
God warned them that a king would cause them trouble, that having God as king was better, but they would not listen. Recall earlier that in the first 200 years as an independent nation, with God as king, that there had only been 4 short wars. Now things were going to be different. Rarely would there be a king who would not be at war with the neighboring countries, and always would the king oppress his own people.
Nowhere in the Old Testament are we told explicitly how long Saul reigned. (Though some translations introduce this interval at First Samuel 10:1.) The reference to the length of time Saul reigns before David is given in Acts 13:21 as 40 years.
The article Timeline: Judges showed that this interval began on 9907-08 AA. So the end of this 40 years must have been 9947-07 AA.
Note some odd things with regard to this passage. Saul is anointed by Samuel. This appears to be within the time allotted to Saul’s reign. Also note that Saul’s son Ish Bosheth is age 40 when he reigns and that he reigns for two years.
Since Acts records Saul being followed by David and since it ignores Ish Bosheth, we must reconcile what the author of Acts had in mind. It appears that Acts is indicating that it was 40 years that the "house of Saul" would reign before David. This is an acceptable meaning. For proof of this, consider that the Angel told Mary before Jesus was born that Jesus would sit on David’s throne, which, of course, at that point did not have David still sitting on it.
This suggests that Ish Bosheth rules from 9945-08 AA through the end of the house of Saul’s 40 years in 9947-07 AA. It also suggests that Ish Bosheth’s 40 years before reign are 9905-08 AA through to the month before his reign.
The Bible records quite a few details of David’s life especially chronological details. To finish our chronological gap we need only a couple details.
Scripture makes clear two very important points, that David ruled in Hebron for 7 years, 6 months    and for the remainder of his 40 year reign he reigned in Jerusalem.   
This change in venue for his reign suggests that Saul and for the last couple years Ish Bosheth were reigning in Jerusalem while David was in Hebron. This also suggests that David and Saul were reigning at the same time in different places.
This is probably why the Old Testament does not touch this issue, it wants to let David rule alone, without "interference" from Saul.
To finish the chronology all we need do is stitch David’s time into the times we have already shown. David spends 7 years 6 months in Hebron, and then goes to Jerusalem. Saul’s house, as we have already established, rules through 9947-07 AA so David must have ruled through this same month in Hebron. 7 years, 6 months earlier, would be 9940-02 AA as the first month of reign.
Since we know David reigned 40 years  the last month of his reign would be 9980-01 AA. Compare that with what we found earlier that Solomon started construction of the Temple in 9980-02 AA and we have a match. Note some things. This says that Solomon must have reigned at the same time as David.
David would live to be the oldest of all the kings we have ages for. He would have been frail. Because of an attempt to steal the throne David anointed Solomon, which is probably when the co-reign started. David’s heart was to build God a temple for the Ark. Because David had shed blood God would not allow him to do that, though David would design it and do much of the preparation. That David’s life ends in the month before Solomon starts the building process suggests that Solomon, and the rest of the workers already assembled to do the work, were waiting patiently for David to die. This probably happened around the Passover time in the year 9980 AA.
Solomon would complete the temple, which David so carefully prepared, in the events of Solomon’s reign.
The main event of Solomon’s reign is the construction of the temple. Solomon would not endure war for this time so that he could accomplish the work set before him to do. We are told that Solomon would work 20 years on both the Temple, and on the Palace, 7 of those 20 on the Temple, 13 on the palace.    
We have further details that the temple itself was completed in the 11th year 8th month of Solomon’s reign or 9987-08 AA. The remaining 13 years, like the remaining 33 years in David’s reign, being fractional, but recorded as full years.
Since he started this great adventure in 9980-02 AA his last month of work on this great project was 20 years later, or 10000-01 AA. This is the month of Passover, and scripture is probably trying to tell us that this temple, the first temple, was finished, with a first Passover celebrated, 10,000 years from Adam.
The remainder of Solomon’s reign is uneventful, from a chronological perspective. Since he reigns 40 years  the last year of his reign is 40 after the start. 9977 AA + 40 - 1 = 10016 AA.
We have covered the biblical chronology through the time of Solomon’s reign. From this point on the chronology shifts to the kings of Jerusalem alone, having lost the Northern Kingdom in a civil war.
1. F. Samuel 10:1
2. S. Samuel 2:10
3. S. Samuel 2:10
4. Acts 13:22
5. Luke 1:32
6. F. Samuel 5:4
7. S. Samuel 2:10
8. S. Chronicles 2:4
9. S. Chronicles 2:4
10. F. Kings 2:11
11. S. Chronicles 29:27
12. S. Kings 5:4
13. F. Chronicles 29:27
14. F. Kings 6:38
15. F. Kings 7:31
16. F. Kings 9:10
17. S. Chronicles 8:1
18. S. Chronicles 9:30
19. F. Kings 11:42