There Will Never Be Another You follows an A B A C form, where the C section begins like the B section, and could be considered a cadential variation. I use the standard key of Eb major for the melody of this reharm. The three tonal centers of the tritonic grouping are C, Ab, and E. There is a six measure sequence which repeats into the fourth bar of the B section. The sequence is shortened to end the B section, and its use produces the similarity in the beginning of the C section.

I had to tweak the melody quite a bit in all three sections. The pickup note Bb is changed to B natural. In bar three of the A section, the F is replaced by E natural on beats one and two, and moved to the F on beat three. Bar four begins with F#, which changes to G on beat three. In bar six, the second C natural is changed to a B natural, to form the melody sequence C, Eb, B, Bb. In the last measure of A, the Bb is moved up to a B natural. In measure one of the B section and the C section, the C natural is changed to a Cb. In measure two of those sections, the F natural is moved up to F#. In measure four of the B section, the Eb is moved up to E natural. In measure five of the C section, the D is changed to Db, and the C is changed to Cb. In measure six, the Ab is moved up to A natural. 

The E chord on the last bar of the C section can serve as the fine.  Here are my changes: