These are the songs that reached number one on the Top 50 Best Sellers chart in 1956 as published by Cash Box magazine.
Issue date Song ArtistJanuary 7"Sixteen Tons"Tennessee Ernie FordJanuary 14"Memories Are Made of This"Dean MartinJanuary 21January 28February 4"The Great Pretender"The PlattersFebruary 11February 18February 25"Rock and Roll Waltz"Kay StarrMarch 3March 10"Lisbon Antigua"Nelson Riddle & OrchestraMarch 17March 24"The Poor People of Paris"Les Baxter & OrchestraMarch 31April 7April 14April 21"Heartbreak Hotel"Elvis PresleyApril 28May 5May 12May 19May 26June 2"Moonglow and Theme from 'Picnic'"Morris Stoloff & Columbia Pictures Orchestra, George Cates & OrchestraJune 9June 16"The Wayward Wind"Gogi GrantJune 23June 30July 7July 14"I Almost Lost My Mind"Pat BooneJuly 21"The Wayward Wind"Gogi GrantJuly 28"I Almost Lost My Mind"Pat BooneAugust 4"My Prayer"The PlattersAugust 11August 18"Hound Dog"Elvis PresleyAugust 25September 1September 8September 15"Don't Be Cruel"September 22September 29October 6October 13October 20October 27"Love Me Tender"November 3November 10November 17November 24December 1"Singing the Blues"Guy MitchellDecember 8December 15December 22December 29
See also 1956 in music List of number-one singles of 1956 (U.S.)
References http://www.cashboxmagazine.com/archives/50s_files/1956.html