The way I see it, if you want the rainbow, you gotta put up with the rain.
Analysis
The exact line appears in the second verse of the song, as written and performed by Dolly Parton. The lyric is widely documented in official song lyrics and recordings. There is no dispute over its origin or accuracy.
Background
'Coat of Many Colors' is an autobiographical song by Dolly Parton, released in 1971, reflecting on her childhood and the metaphorical significance of a coat made from rags. The song is one of her most iconic works and has been covered and referenced extensively.
Verdict summary
Dolly Parton did sing the lyric in her 1971 song 'Coat of Many Colors'.
Sources consulted
— Dolly Parton – Coat of Many Colors (Official Lyrics Video), Sony Music Nashville, 1971
— Genius Lyrics – Dolly Parton – Coat of Many Colors (https://genius.com/Dolly-parton-coat-of-many-colors-lyrics)
— Songfacts – Coat of Many Colors by Dolly Parton (https://www.songfacts.com/facts/dolly-parton/coat-of-many-colors)