These are the songs that reached number one on the Top 50 Best Sellers chart in 1953 as published by Cash Box magazine.
Issue date Song ArtistJanuary 3"I Saw Mommy Kissing Santa Claus"Jimmy BoydJanuary 10"Why Don't You Believe Me"Joni JamesJanuary 17"Don't Let The Stars Get In Your Eyes"Perry ComoJanuary 24January 31February 7"Till I Waltz Again with You"Teresa BrewerFebruary 14February 21February 28March 7March 14March 21"The Doggie in the Window"Patti PageMarch 28April 4April 11April 18April 25May 2May 9"The Song from Moulin Rouge"Percy Faith & OrchestraMay 16May 23May 30June 6June 13June 20June 27July 4"I'm Walking Behind You"Eddie FisherJuly 11July 18July 25August 1August 8August 15"No Other Love"Perry ComoAugust 22"Vaya con Dios (May God Be With You)"Les Paul and Mary FordAugust 29September 5"Crying in the Chapel"June ValliSeptember 12"Vaya con Dios (May God Be With You)"Les Paul and Mary FordSeptember 19"Crying in the Chapel"June Valli, Darrell Glenn, Rex Allen, The OriolesSeptember 26October 3"You, You, You"The Ames BrothersOctober 10"Vaya con Dios (May God Be With You)"Les Paul and Mary FordOctober 17October 24"St. George and the Dragonet"Stan FrebergOctober 31November 7November 14"Rags to Riches"Tony BennettNovember 21"Eh, Cumpari"Julius La RosaNovember 28"Rags to Riches"Tony BennettDecember 5December 12December 19December 26"Oh My Pa-Pa (O Mein Papa)"Eddie Fisher, Eddie Calvert
See also 1953 in music List of number-one singles of 1953 (U.S.)
References https://web.archive.org/web/20110818052004/http://cashboxmagazine.com/archives/50s_files/1953.html