When was David born? I would like to know when David, the king of Israel, was born.
David was born 1041 bc, maybe plus or minus a year.  

David was 30 years old when he began to reign and he reigned 40 years.(2 Sam 5:4)

Multiple lines of evidence put the end of his reign/start of the reign of Solomon at 971 BC.

The evidence is found in:- 
1. Edwin Thiele's "Mysterious Numbers of the Hebrew Kings";


William Hamilton Barnes evidence from the Tyrian King Lists;
Kenneth Kitchen's evidence from Egyptian chronology;
1 Kings 6:1, Ezekiel 40.1 and Leviticus 25:9,10, together with 
the Seder Olam.


The Seder Olam probably written in the second century AD says that Ezekiel's Jubilee in Ezekiel 40:1 was the 17th.  It was a Jubilee Year because in that year New Year's day, Rosh Hashanah, was on the 10th day of the month (see Leviticus 25:9,10). For 48 out of 49 years New Year's Day happens on the 1st day of the month.  The Jubilee Year happens every 49 years.  Ezekiel 40:1 is counted from the destruction of Jerusalem 587 BC, and was in 573 BC.

A translation of the Seder Olam says:


  And so it says (Ez. 40:1): “In 25th year of our exile, on the day of the New Year, on the tenth of the month, 14 years after the destruction of the of Jerusalem.” When did he Ezekiel have this vision? At the beginning of a Jubilee period. If they staid for 17 entire jubilee periods, how can there be an excess of 17 years? 


See http://www.betemunah.org/sederolam.html and look at the section in part 2 under Joshua (chapters 11 and 12), and the paragraph starting "Caleb said to Joshua "I was 40 years old when Moses..", etc.

The author of the Seder Olam does not know how to find 17 "extra" years from the time of the beginning of the Jubilee Cycle to the 14 year after the destruction of Jerusalem (in 587 BC).  These difficulties of the author of the Seder Olam are not important to us.  What is important is that he says there were 17 jubilee cycles: for this assertion he must have had access to information held by the priests in Jerusalem which no longer exists.

573 BC + (17 jubilees * 49 years) = 573 + 833 = 1406 (year of entry into Canaan and year the Jubilee cycles first began)

1406 + 40 years in the wilderness = 1446 (date of exodus)

1446 - 479 (as per 1 Kings 6:1) = 967 BC (Temple of Solomon started to be built)

967 BC + 4 (as per 1 Kings 6:1) = 971 BC (Start of Solomon's, end of David's reign)

971 +70 (as per 2 Samuel 5:4) = 1041 BC (year of David's birth).

3 Extra Biblical evidences of the existence of David:-

In 1993 AD the "House of David" inscription was found at Tell Dan, the first extra Biblical evidence that David actually existed.  The inscription related to events in the year 841 BC, and defeat of Ahaziah.  "We thus gain a clear mention of David as dynastic founder of the kingdom of Judah about 150 years after his death". (See "On the Reliability of the Old Testament" by Kenneth Kitchen, Eerdmans, (2003), pages 92,93 and 615).

The stela of Mesha king of Moab also mentions the "House of David" from about the same time.  "This was some six generations after his (David's) death" (Kitchen, page 93).

Shoshenq I of Egypt lists his achievements at Karnak.  One of the places he speaks of which is in south Judah/Negev region is a place called "Heights of David".  This would have been within 50 years of David's death.  (Kitchen, p93)

Postscript:
I should have provided a link to the archaeologist Eilat Mazar's article, first published early 2006:  "Did I find King David's Palace?" :-
https://www.biblicalarchaeology.org/daily/biblical-sites-places/jerusalem/did-i-find-king-davids-palace/