Others have already mentioned "No Other Love"--the new "Victory at Sea" book has all the timeline details. Rodgers's tango was one of his twelve melodies for the series, composed in July 1952. Who knows when he might have considered using it in a future show, but by early 1953 Hammerstein starts placing the song in his "Me and Juliet" script drafts, and the completed song (with Hammersetin's added lyric) was copyrighted in April 1953, less than a week before the musical opened out of town in Cleveland.
***********************************
The "ALWAYS" in the original question is the troublemaker; "usually" or "conventionally" has always served well.
