I just play F, C, Em, and Am throughout the entire song.


F                                     C
You had my heart and we'll never be world's apart...
Em                                   Am
Maybe in magazines, but you'll still be my star.

Same chords...
             F                         C
'Cause I'm singing in the rain, just singing in the rain
           Em                 Am
What a glorious feelin', I'm happy again. 
  F                        C
I'm laughing at clouds so dark up above.
     Em                     Am 
I'm singing-singing in the rain.