William Rufus King was a relatively minor and short-serving Vice-President. We do not know his religious affiliation. Further research and information is needed.
William R. King was the only unmarried Vice-President. He died never having married. He had no children.
From: "William Rufus King" article on Wikipedia website (http://en.wikipedia.org/wiki/William_Rufus_de_Vane_King; viewed 23 November 2005):
William Rufus de Vane King was a U.S. Representative from North Carolina, a Senator from Alabama, and the thirteenth Vice President of the United States. He was the shortest-serving person to occupy that office (45 days) without becoming President. (John Tyler was the shortest-serving, with Andrew Johnson also serving less time than King.)
...Some historians have speculated that King may have been gay, and that he had a long-term intimate relationship with James Buchanan (it is not disputed that the two lived together for a time in Washington, D.C.). It is also said that King's detractors in the Senate referred to him as "Miss Nancy." The theory is controversial and a source of debate among Buchanan and King historians. Historian and author James W. Loewen is one of the theory's better-known proponents.