James Fryer: "It's originally a Jamaican folk song."

While you may have experienced a local cover, the true original is straight Tin Pan Alley, no chaser. The writing team of "(Gilbert, Charles)" mentioned in Sorchas post above is fairly well documented as Russian-American Louis Wolfe Gilbert (as L. Wolfe Gilbert: "Waiting for the Robert E. Lee", etc) and Bahamian Charles Leonard Lofthouse (as L. Charles aka Charles Lighthouse: "Bahama Mama", "Delia Gone", etc.) The original copyright was issued in the United States in 1932.