According to Book of Mormon Geography expert Duane R. Aston, Phd, the Two Cumorah theory began with Sidney Sperry:

It was not until the 1960’s that it became clear that the Hill Cumorah of wesern New York was simply too far from central America to fit in with the idea that Jaredites and Nephites had landed in central America and later migrated to New York. In a nutshell, this is what happened.

1. Sidney Sperry made an analysis of the Limhi account wherein an expedition was sent out from the land of Nephi in the south. Their destination was Zarahemla, further to the north. Scholars agree that distance factors would place Zarahemla from one to two hundred miles from the land of Nephi.

2. The expedition over-shot its mark and ended up in a land of many waters where the Jaredites had lived. They found ruins of buildings, hilts of swords, evidences of a terrible destruction, and twenty-four plates that were the record of the Jaredites. Therese artifacts were assumed to have been left by the Jaredites who were destroyed at Hill Cumorah.

3. Thus Sperry’s analysis of the Limhi expeditin account made it clear that the land of Cumorah must be not all that far from the land of Zarahemla. Since the expedition thought that they had discovered the land of Zarahemla, with the distance measured only in a couple hundred miles at most, and not the nearly three thousand miles from Central America to Hill Cumorah in western New York.

Recognizing the impact of Sperry’s findings, Book of Mormon geographers were faced with a dilemma. Either the land of Nephi and Zarahemla were close to Hill Cumorah in New York, or another Hill Cumorah was close to Zarahemla and the land of Nephi in the assumed setting located in Central America.

Instead of accepting that the geography of the Book of Mormon should be associated with the Hill Cumorah of New York, the geographers maintained interest in Central America. Thus it became necessary to theorize that there had to be another Hill Cumorah located somewhere in Central America.

The consequences are inevitable; proposing the existence of another Hill Cumorah somewhere in Central America leads to confusion because most members of the Church know of only one Hill Cumorah (Duane R. Aston, Return to Cumorah, 1998, pp. 12-13).

The following comes from Aston’s endnotes:

His conclusion was that the “Book of Mormon evidence points inevitably to a Ramah-Cumorah in Middle America.”

Now, if a narrow neck of land had been recognized to exist in western New York, might this have made a difference on Sperry’s interpretation? It would seem that not recognizing a narrow neck of land in western New York may have been germane to the origins of the two-Cumorah theory (p. 19).

[Source: http://maxwellinstitute.byu.edu/publications/jbms/?vol=4&num=1&id=98]