These are the songs that reached number one on the Top 100 Best Sellers chart in 1959 as published by Cash Box magazine. +KeyIndicates best-performing single of 1959
Issue date Song ArtistJanuary 3 The Chipmunk Song Chipmunks with David SevilleJanuary 10 January 17 Smoke Gets In Your Eyes The Platters January 24 January 31 February 7 February 14 Stagger Lee Lloyd Price February 21 February 28 March 7 Venus Frankie AvalonMarch 14 March 21 March 28 April 4 April 11 Come Softly To Me The Fleetwoods April 18 April 25 May 2 May 9 The Happy Organ Dave "Baby" CortezMay 16 May 23 Kansas City Wilbert Harrison May 30 The Battle of New Orleans Johnny HortonJune 6 June 13 June 20 June 27 July 4 July 11 July 18 July 25 August 1 Lonely Boy Paul Anka August 8 August 15 There Goes My Baby The DriftersAugust 22 August 29 The Three Bells The BrownsSeptember 5 September 12 September 19 September 26 Mack the Knife Bobby DarinOctober 3 October 10 October 17 October 24 October 31 November 7 November 14 Mr. Blue The FleetwoodsNovember 21 Don't You Know? Della ReeseNovember 28 Mr. Blue The FleetwoodsDecember 5 Don't You Know Della ReeseDecember 12 Mack the Knife Bobby DarinDecember 19 Heartaches By The Number Guy MitchellDecember 26
See also 1959 in music List of Hot 100 number-one singles of 1959 (U.S.)
References http://www.cashboxmagazine.com/archives/50s_files/1959.html