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 760BCE, 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), this earthquake 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.
Conversely, my chart shows Uzziah's sole reign beginning in 767BCE, 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 765BCE to 751BCE, which agrees perfectly with the geologists' findings.
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.