Francis Patrick Carney (September 20, 1846 – May 4, 1902) was the tenth Lieutenant Governor of Colorado, United States. He was a member of the Populist party and served from 1899 to 1901 under Governor Charles Spalding Thomas.
He was born September 20, 1846 in County Fermanagh, Ireland. His family emigrated to New York City in 1859 and moved to Ouray, Colorado in 1877. He became a mason and worked as a contractor and miner as well as an organizer of labor unions. He served as a Colorado Assemblyman from 1893 to 1895 and state senator 1895 to 1899. He died May 4, 1902 in Ouray.