The tune for No Other Love was originally part of Richard Rodgers' score for the acclaimed 1952 TV war documentary series Victory at Sea. In the orchestral suite compiled from the score the piece was titled Beneath the Southern Cross.
https://www.youtube.com/watch?v=sDuQ...=RDsDuQp_AfVJk

In 1953, Rodgers "borrowed" his own tune and included it in the Rodgers and Hammerstein musical Me and Juliet as No Other Love, with lyrics by Hammerstein.

It was a hit tune for Perry Como:
https://www.youtube.com/watch?v=kfiSbyF5YYE

It was even recorded by Jay and the Americans:
https://www.youtube.com/watch?v=77h84WomwKM
Personal note: My band and I played for Jay Black's son's wedding.

My version takes liberties with some of the harmonies for more of a jazz flavor. A lead sheet for the standard version can be found in Hal Leonard's Ultimate Broadway Fake Book, and others.

No Other Love-Rev JE - Richard Rodgers

Cheers,
Jer