John Quincy Adams, Franklin Pierce, Rutherford Hayes, Theodore Roosevelt, Lyndon Johnson.
Here's one: President Pierce:
"The Constitution offers a choice. Presidents may "swear" (on a Bible) or "affirm" their oath (on some other book). Two months before Franklin Pierce became President, his family -- having already lost two children to typhus -- was involved in a train wreck in which their only surviving child, thirteen-year-old Benjamin, was crushed to death. Jane Pierce believed the accident was a punishment from God for her husband's acceptance of the presidency. As a result, Pierce chose to "affirm" his oath of office on a law book rather than the Bible. An image of Pierce's swearing-in is available through The American President. (Most presidents, with perhaps three of four exceptions, have elected to use the Bible in their inauguration.)"

Also, Teddy Roosevelt, darling of confused conservatives:September 14, 1901 -- Theodore Roosevelt
1.The only President not sworn in on a Bible. Mr. Ansley Wilcox, at whose home Roosevelt took the oath of office, wrote in 1903, "According to my best recollection no Bible was used, but President Roosevelt was sworn in with uplifted hand." (The Presidents and Their Wives, p. 3)
He also tried to get "In God We Trust" taken off our coinage. Bully for him!*
Also, apparently, President Hayes, who was too religious to do it on a Sunday so had two swearing in's on Saturday and Monday. The first one was bible-free.*Here's another spin that includes John Quincy Adams and maybe a lot more:" John Quincy Adams, according to his own letters, placed his hand on a constitutional law volume rather than a Bible to indicate where his fealty lay.... There are no known inauguration Bibles for presidents John Adams through John Tyler; in fact, there's no concrete evidence that those early presidents used a Bible at all for the oath." from Slate
LBJ. He was on Air Force One and Lawrence O'Brien grabbed what he thought was a bible from beside the President's bed (that would have been Kennedy) but it turned out later to be a Catholic missal instead.
Other quirks, President Kennedy was the first and only one to swear on the Catholic version of the Bible ( Probably in Latin since there was no official English one at the time), and Nixon used two Bibles for some reason.
As far as I can see, the current record is two swearing in's per term in office, and two bibles per swearing in. If Obama decides to do a third swearing in this time on three bibles, he could earn a place in the Guinness book of records. Maybe someone should tell him.
ps. That reporter should have checked on mahalo

"Theodore Roosevelt did not use a Bible when taking the oath in 1901. Dwight Eisenhower, Harry Truman, and Richard Nixon swore the oath on two Bibles. John Quincy Adams swore on a book of law. Lyndon B. Johnson was sworn in on a Roman Catholic missal on Air Force One."