Crockett, in his Harmony of Samuel, Kings, and Chronicles, places the national assembly that acclaimed Solomon king (1 Chronicles 23-29) before Absalom's rebellion, which he places in David's 40th year in accordance with 2 Samuel 15:7 (KJV and Hebrew manuscripts). Consequently, Crockett says that Solomon was made king the second time in 1 Kings 1.
Crockett's chronology creates several problems. To begin with, 1 Chronicles 29:22 says that Solomon was made king the second time at the great national assembly, which would place it after 1 Kings 1. Second, the assumption in 1 Kings 1 is that there had been no national proclamation making Solomon king at the time Adonijah wished to seize the throne. Bathsheba reminded David only of a promise he had made her regarding Solomon. Furthermore, she said that all Israel was waiting for David to make his wishes about a successor known (1 Kings 1:20). Finally, Absalom's rebellion was directed against David, not Solomon. After Absalom was killed, the people spoke of recalling David, not Solomon.
The one justification for Crockett's chronology is 2 Samuel 15:7 which says that Absalom requested permission to fulfill a vow in Hebron "at the end of forty years." This statement appears rather odd because throughout the Absalom narrative, time references relate to the events within the narrative. Thus, two years after Amnon raped Tamar, Absalom killed Amnon (2 Samuel 13:23). After Absalom had lived in Geshur for three years, he was recalled to Jerusalem (2 Samuel 13:38) but he did not see the king for another two years (2 Samuel 14:28). Then, all of a sudden, there is this reference to 40 years which must begin sometime before the Absalom narrative began. Although Crockett takes it to refer to the beginning of David's reign in Hebron, there may be a better solution. The Syriac, some Septuigint manuscripts, and Josephus read "four" instead of "forty" in 2 Samuel 15:7. This reading would then continue the trend within the narrative to relate the events to each other. Furthermore, this reading would complete the narrative by connecting all the events from the rape of Tamar to the death of Absalom. If "four years" is the correct reading, then the Absalom narrative covers about eleven years, or twenty-five percent, of David's forty-year reign.