Anwser: Henry Stanbery.

  The Congressional Research Service explains:

On April 16, 1866, President Andrew Johnson nominated Henry Stanbery to replace John Catron, who had died the previous May. By the time Stanbery was nominated, however, the House of Representatives had passed a bill decreasing the number of justices in the Supreme Court. The act, as signed into law on July 23, 1866, called for a decrease in the number of Associate Justices from nine to six through the process of attrition. At the time the bill was initiated and also at the time its final version was signed, only one vacancy, that to which Stanbery was nominated, existed on the Court. Eight Associate Justice positions remained on the bench until the death of James M. Wayne in July 1867. Seven Associate Justice positions remained until a law was passed in April 1869 to increase the number back to eight.

  Stanbery was nominated for a vacancy that was never filled, because it was eliminated by Congress. (I'm assuming that when the Supreme Court was expanded again, the new seat wasn't the same one that was eliminated, thus recreating the vacancy. A debatable point, maybe. But hey, it's good enough for a trivia question.)

  Thanks to Ed Whelan for the link.