This idea is actually not so much a theory of the first landfall, as it is a theory of the transatlantic track of the first voyage, and is included here for the sake of completeness. It was proposed by Dr. Luis M. Coin Cuenca in John Dyson's 1991 book, Columbus: for gold, God, and glory. Belief in this theory requires a mindset that sees vast conspiracies behind every important historical event.
Dr. Coin bases his theory on Columbus's logged observation that the Atlantic currents were against him on September 13, 1492. Coin correctly notes that this is unusual in the area that Columbus was supposedly traversing at the time, and uses this unlikelyhood to suppose that Columbus actually sailed SW (instead of the logged W) from Hierro. The reason that the log says W, according to Coin, is that the log was altered to avoid the appearance of Spanish incursion into the Portuguese sphere of influence.
The problem that Coin overlooks: SE-setting currents are even less likely in the area that Coin has Columbus sailing through, than in the area that everyone else assumes. In other words, Coin fails to address the very problem he himself raised. Currents in the open ocean, like winds in the atmosphere, often move in directions different from, or even contrary to, the prevailing direction; see the section on Columbus's transatlantic track.
Dr. Coin also makes a big deal of bird sightings recorded in the log, in areas of the Atlantic which (according to Dr. Coin) no birds are found. But recent research by John Parker (1992) has identified nearly all of these sightings with their correct species, and in areas that they are known to exist.
Coin uses the alleged log-fixing to put Columbus in sight of the Virgin Islands on September 25, which the fleet bypasses in the night. Then Coin has the fleet sailing WNW, missing all remaining islands until the "real" landfall of October 12, at some unspecified point in the Bahamas. This northward movement is attributed to northward setting currents of five knots, twice the speed of the Gulf Stream, and five or ten times the typical current speed in that area.
The publication of this theory in 1991 attracted immediate ridicule by Joseph Judge in the pages of The World & I, to which Dyson offered a wounded response. As I've said before, any island can be the landfall provided only that one re-writes the log to conform to one's pet theory. Coin and Dyson prove this in spades.
So, in addition to all the inter-Bahamian problems, Coin adds a bunch to whatever list you prefer.