John Nance Garner was a Protestant. Further research is needed in order to identify his specific denominational affiliation.
From: Political Graveyard website (http://politicalgraveyard.com/bio/garner.html#R9M0IXQ9K; viewed 29 November 2005):
Garner, John Nance (1868-1967) - also known as "Cactus Jack" - of Uvalde, Uvalde County, Tex. Born near Detroit, Red River County, Tex., November 22, 1868. Democrat. Lawyer; county judge in Texas, 1893-97; member of Texas state house of representatives, 1898-1902; delegate to Democratic National Convention from Texas, 1900, 1904, 1916, 1924; U.S. Representative from Texas 15th District, 1903-33; elected unopposed 1920, 1922, 1924; Speaker of the U.S. House, 1931-33; candidate for Democratic nomination for President, 1932; Vice President of the United States, 1933-41. Died in Uvalde, Uvalde County, Tex., November 7, 1967. Interment at Uvalde Cemetery, Uvalde, Tex.
Books about John Nance Garner: O. C. Fisher, Cactus Jack: A Biography of John Nance Garner (for young readers); Maurine Walpole Liles, The Boy of Blossom Prairie Who Became Vice-President (for young readers, out of print)