I just play F, C, Em, and Am throughout the entire song.
 
FC You had my heart and we'll never be world's apart...
EmAm Maybe in magazines, but you'll still be my star.
 Same chords... 
FC 'Cause I'm singing in the rain, just singing in the rain
EmAm What a glorious feelin', I'm happy again.
FC I'm laughing at clouds so dark up above.
EmAm