Amos 1:1 is set during the reigns of both Uzziah and Jeroboam II, “two years before the earthquake”. Geologists* have dated this earthquake to around 760 BCE, with an error margin of plus or minus 25 years.
*Steven A. Austin, Gordon W. Franz, and Eric G. Frost, “Amos’s Earthquake: An Extraordinary Middle East Seismic Event of 750 B.C.” International Geology Review 42 (2000) 657–671. Y. Yadin, Hazor, the Rediscovery of a Great Citadel of the Bible (New York: Random House, 1975). I. Finkelstein, “Hazor and the North in the Iron Age: A Low Chronology Perspective,” Bulletin of the American Schools of Oriental Research 314 (1999) 55–70. D. Ussishkin, “Lachish” in E. Stern, ed., The New Encyclopedia of Archaeological Excavations in the Holy Land (New York: Simon & Schuster, 1993) vol. 1 338–342.)
According to Insight (volume 1, page 99), Amos’ prophecy occurred “sometime within the 26-year period from 829 to about 804 B.C.E.,” at least nineteen years before the earliest point within the margin of error for the earthquake. Insight provides no source for the dating of the earthquake, instead simply asserting that it must have occurred within two years of the period the Watch Tower Society assigns for the overlap of the two reigns.
An independent comparison of the Bible confirms that Uzziah’s sole reign began in 767 BCE (after a co-regency with Amaziah beginning in 790 BCE), and Jeroboam’s final year overlaps Uzziah’s reign in 753 BCE. Because Amos says his writing is during those two reigns but two years before the earthquake, that would place the earthquake itself within the range of 765 BCE to 751 BCE, which agrees perfectly with the geologists’ findings.*
*See pages 5 and 6 of timeline from 1048 BCE to 515 BCE (PDF).
An article by archaeologist helps to further identify the relevant Iron IIB period. The article confirms that the ages of artifacts found in the geological strata were determined based on carbon dating, independently from when particular kings are expected to have reigned. The article associates the earlier Iron IIA period with the period up to the end of the 9th century, placing Iron IIB well into the 8th century BCE. Israel Finkelstein, Professor of the Archaeology of Israel in the Bronze Age and Iron Ages at Tel Aviv University, quite definitely dissociates the earthquake from the Iron IIA period, noting, “Finally, from the ceramic point of view, it is impossible to equate Iron IIA Lachish IV and Arad XI with Iron IIB Hazor VI.” In another article, Finkelstein provides a diagram confirming that carbon dating establishes the transition to the Iron IIB period after 800 BCE.
This is yet another area where the Watch Tower Society must throw its hands up in the air and claim all the experts must just be wrong.