All sources point to the same thing: The Bible in the picture is the one that Eisenhower used. It was an American Standard Version, a version used by Witnesses before the New World Translation because it contained "Jehovah" in the Old Testament.
When you look at the following website, http://memory.loc.gov/ammem/pihtml/pibible.html, it says in the notes for the second inauguration of Eisenhower:
12. New York Times, Jan. 22, 1957, p. 16. (Return to text)
And the NYT, Jan 22, 1957, p.16 said:
"The President's Bible, given him by his mother on his graduation from the United States Military at West Point, N.Y.,"
So it IS the one shown in the picture.