A plain, literal Biblical chronology for the 8th century BC would go something like this:
Amaziah of Judah (29 years): 840-812 BC.
Jeroboam II of Israel (41 Years, from Year 15 Amaziah): 825 BC-784 BC (11 hanging years between him and successor)
Uzziah of Judah (52 years, from Year 27 of Jeroboam II): 811-759/58 BC
Zachariah of Israel (6 months, Yr 38 Uzziah): 773 BC
Shallum of Israel (1 month, Yr 39 Uzziah): 772 BC
Menahem of Israel (10 years, Yr 39 Uzziah): 772-762 BC
Pekahiah (2 years, Yr 50 Uzziah): 762-760 BC
Pekah of Israel (20 years, Year 52 of Uzziah): 760-740 BC (8 hanging years between him and successor)
Jotham of Judah (16 years, from Year 2 Pekah): 759-743 BC
Ahaz of Judah (16 years, from Year 17 of Pekah): 744-728 BC
Hoshea of Israel (9 years, “Year 20” of Jotham, “Year 12” Ahaz):732-723
Hezekiah of Judah (29 years, from Year 3 of Hoshea): 727-798 BC
The problems with this unedited chronology are, of course, that there are hanging years without a king in Israel and that this makes Biblical Chronology contradict the Mesopotamian and Egyptian Chronological Pillars:
1. The Battle of Qarqar in 853 BC, at which Shalmaneser III of Assyria listed Ahab of Israel as one of his foes (see the further discussion below).
2. The tribute of Jehu of Israel to Shalmaneser in 841 BC.
3. The invasion of Sennacherib in Hezekiah’s 14th year, 701 BC.
4. The death of King Josiah in 609 BC.
5. Nebuchadnezzar’s initial capture of Jerusalem in 605 BC, at which time Daniel and other Judeans were taken to Babylon.
6. The second capture of Jerusalem and its king Jehoiachin by Nebuchadnezzar—the exact date of which is given in the Babylonian Chronicle as 2 Adar, i.e. March 16, 597 BC.
Therefore, it seems a chronology with more co-regencies should be preferrable, as the one advocated by Thiele:
Amaziah of Judah:796-776
Jeroboam II of Israel:791-750
Uzziah/Azariah of Judah:787/76-736
Zachariah of Israel:750
Jotham of Judah:750-734
Shallum of Israel:749
Menahem of Israel:749-738
Pekahiah of Israel:738-736
Pekah of Israel:736-732
Ahaz of Judah:744 (2 Kings 16:2, 17:1) or 35 (2 Kings 16:1) -727 (Is 14:28-29)
Hoshea of Israel:732-723
The date for Menahem fits with Tiglath-Pileser’s identification with Biblical Pul. A solar eclipse in what Hezekiah’s 14th year (714 BC) probably reflects the shadow going back in 2 Kings 20:11, and was probably artificially associated by the Deuteronomist with the events of 701 BC, leading scholars to invent imaginary co-regencies between Ahaz, Hezekiah, and Manasseh, placing Hezekiah from 715-687 BC, contradicting 2 Kings 20:21 and 2 Kings 18:1-10, unambiguously placing Hezekiah from 727 to 698 BC.