I think these are pretty accurate chords. To play it like the Fiona track, pay attention 
to inversions. Enjoy!

[Note: Fdim7/Db can also be thought of as Db7(add9)]

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Fiona Apple - Pale September

Ab6 (xx1111@1)    Cdim (2312xx@1) Ab6 (xx1111@1)                            CdimPale (2312xx@1)September, I wore the time like a dress that year
Ab6 (xx1111@1)             Cdim (2312xx@1) Ab6 (xx1111@1)                         CdimThe (2312xx@1)autumn days swung soft around me, like cotton on my skin
Ab6 (xx1111@1)              Cdim (2312xx@1)   Ab6 (xx1111@1)                            CdimBut (2312xx@1)as the embers of the summer lost their breath and disappeared
Ab6 (xx1111@1)                 Cdim (2312xx@1)   Ab6 (xx1111@1)                          CdimMy (2312xx@1)heart went cold and only hollow rhythms resounded from within
Fdim7          Fdim7/Db
But then he rose, brilliant as the moon in full
Fdim7                         Fdim7/Db
And sank in the burrows of my keep
    F# (244322@1)   Absus4 (xx1124@1)  Ebm7 (x3131x@4)    F# (244322@1)   
Absus4   Ebm7
And all my armor falling down, in a pile at my feet
    F# (244322@1)   Absus4 (xx1124@1)Ebm7 (x3131x@4)   Absus4 (xx1124@1) F# (244322@1)   
    Absus4 (xx1124@1)  Ebm7And (x3131x@4)my winter giving way to warm, as I'm singing him to sleep

Cdim
Ab6 (xx1111@1) Cdim (2312xx@1) Ab6 (xx1111@1)   Cdim (2312xx@1)name="chord_xx1111@1">Ab6   Cdim (2312xx@1) Ab6 (xx1111@1)   Cdim (2312xx@1)Ab6 (xx1111@1)         Cdim (2312xx@1)  Ab6 (xx1111@1)      CdimHe (2312xx@1)goes along just as a water lily
Ab6 (xx1111@1)         Cdim (2312xx@1)  Ab6 (xx1111@1)                        CdimGentle (2312xx@1)on the surface of his thoughts his body floats
Ab6 (xx1111@1)    Cdim (2312xx@1) Ab6 (xx1111@1)               CdimUnweighed (2312xx@1)down by passion or intensity
Ab6 (xx1111@1)              Cdim (2312xx@1) Ab6 (xx1111@1)             CdimYet (2312xx@1)unaware of the depth upon which he coasts
Fdim7      Fdim7/Db
And he finds a home in me
Fdim7                            Fdim7/Db
For what misfortune sows, he knows my touch will reap

F# (244322@1)      Absus4 (xx1124@1)  Ebm7 (x3131x@4)     F# (244322@1)  
Absus4   Ebm7
And all my armor falling down, in a pile at my feet
    F# (244322@1) Absus4 (xx1124@1)  Ebm7 (x3131x@4) Absus4 (xx1124@1)   F# (244322@1)   
Absus4   Ebm7
And my winter giving way to warm, as I'm singing him to sleep

Fdim7    Fdim7/Db   Fdim7    Fdim7/Db

F# (244322@1)    Absus4 (xx1124@1)  Ebm7 (x3131x@4)   F# (244322@1)   Absus4 (xx1124@1) Ebm7All (x3131x@4)my armor falling down, in a pile at my feet
    F# (244322@1)  Absus4 (xx1124@1)  Ebm7 (x3131x@4) Absus4 (xx1124@1)  F# (244322@1)   
Absus4   Ebm7
And my winter giving way to warm, as I'm singing him to sleep
 F# (244322@1)      Absus4 (xx1124@1)  Ebm7 (x3131x@4)   F# (244322@1)   Absus4 (xx1124@1)  Ebm7
All my armor falling down, in a pile at my feet
    F# (244322@1) Absus4 (xx1124@1)  Ebm7 (x3131x@4) Absus4 (xx1124@1)   F# (244322@1)   
Absus4   Ebm7
And my winter giving way to warm, as I'm singing him to sleep

Gb   Absus4   Ebm7...  (repeat to the end)