AlanF had done some excellent (as usual) research on this topic. Some is at this webpage, "Notes On False Prophets, Part I: JW Beliefs About Chronology in the Early Days"
Here is a relevant selection from that page:
Most Jehovah's Witnesses understand that the calculations leading to 1914 as the end of "The Gentile Times," and as the year when Christ invisibly established his kingdom in the heavens are unique to the Watchtower Society. On its inside cover, the 1959 book Jehovah's Witnesses in the Divine Purpose contains these statements:
1870 Charles Taze Russell begins his study of the Bible with a small group of associates.
1877 The book "Three Worlds" is published identifying the date 1914 as the end of "Gentile Times."
The impression given here, as well as in most other Watchtower publications, is that the book Three Worlds (which was written by N. H. Barbour and which Russell only financed) was the first publication to contain this teaching about 1914.
But this is not true at all. In 1823 John Aquila Brown published an explanation virtually identical to the one ultimately adopted by the Society, except that the 2520 years ran from 604 B.C. to 1917 A.D. He foretold that then "the full glory of the kingdom of Israel shall be perfected," but he did not apply the "Gentile Times" to the 2520 years. He also taught that the 2300 days of Daniel 12 would end in 1844. A form of this teaching was taken up by William Miller and his followers, who predicted the end of the world in 1843-1844, and who started the Second Advent movement.
After the failure of the expectations for 1844, Miller's movement split into several sects, one of which eventually formed around N. H. Barbour. Barbour redid Brown's calculations and came up with a period from 606 B.C. to 1914 A.D. (actually this was a miscalculation since this period is only 2519 years. The Society used this calculation until 1943, when 606 was changed to 607 in The Truth Shall Make You Free, pages 238-239, using an incorrect and disingenuous explanation.) Barbour first published the 1914 date in his magazine Herald of the Morning in September, 1875.
In the July 15, 1906 Watch Tower C. T. Russell told how in 1876 Barbour and others convinced him of their 1914 teachings. Russell became assistant editor of Herald of the Morning by July, 1878. This magazine, and later, Russell's Zion's Watch Tower and Herald of Christ's Presence, also published the year 1873 as the end of 6000 years of human history and 1874 as the start of Christ's invisible presence. Among Adventist related groups, the invisible presence doctrine actually started as a result of the failure of Barbour's and other's prediction of 1874 for Christ's return, as shown below. The doctrine allowed them to say, like William Miller before, that they had expected the "wrong thing at the right time." This explanation was later adopted by the Society to explain the failure of its 1914 predictions.
Over at Hearld Magazine's special Bible Sudent's History page, http://www.heraldmag.org/04history_4.htm we have:
E. B. Elliott
Six thousand years end in 1872 / modified chronology from Henry Fynes Clinton.
Elliott?s chronology drawn up and modified slightly by Rev. C. Bowen.
Jubilees end 1874; Gentile Times end 1914.
Nelson H. Barbour
Jewish and Gospel Age Parallels and Harvests, 1845 year doubles.
Published idea of invisible presence in 1874 in his magazine.
Views concerning the prophetic time periods taught by Pastor Russell originated with Barbour. (1,260, 1,290, 1,335, 2,300 day-for-year time prophecies).
The dates, 1798-99, 1828, 1846, 1872, 1874, 1878, 1881, 1914. Taught six thousand years ending in 1872 from E. B. Elliott.
Pastor Charles Taze Russell
First to combine the ideas of time prophecy, chronology, and the purpose of the return of Christ to bless all mankind. Attributed his understandings to some of those listed above.
Barbour's (and Russell's) book, "Three Worlds and The Harvest of this World" (1877) gives the gentile times calculation, which is essentially the same as the JWs use now.
On page 83, the calculation is given:
The seventy years captivity ended in the first year of Cyrus, which was B . C . 536. They therefore commenced seventy years before, or B . C . 606. Hence, it was in B . C . 606, that God's kingdom ended, the diadem was removed, and all the earth given up to the Gentiles. 2520 years from B . C . 606, will end in A . D . 1914, or forty years from 1874; and this forty years upon which we have now entered is to be such "a time of trouble as never was since there was a nation." And during this forty years, the afterwards the spiritual)," the Jews are to be restored, the Gentile kingdoms broken in pieces "like a potter's vessel," and the kingdoms of this world become the kingdoms of our Lord and his Christ, and the judgment age introduced.
It has been researched where and when the WTS added (or rather, subtracted) a 1 to these dates, giving 607 BC, but the essentially idea of tying it to the end of Babylonian capivity (release by Cyrus) is the same.
The "Three Worlds" book may be downloaded from here: http://www.heraldmag.org/olb/contents/history/3worlds.pdf