You're gonna vibrato the root note of the chord, This sounds right to me.
Although i think it's a different D chord, wether it's Dm or another D chord.  

G
Everyboy's got themselves a horseless carraige
C
All the gals talking bout ah appy marraige
D
Here i am living on this dead end street
G                  D
In woe running harder
G                           D
Ain't you gonna cry for me gal
G                      D
Ain't you gonna cry for me 

Falling right down the hill of golden statues
I'm gonna kick em down with my steel potion
And i'm gonna throw em to the dumpster baby and 
Dream about you
Ain't you gonna cry for me gal
Ain't you gonna cry for me

Everyone just wants to be my bastard
To shine their shoes and say well yes sir
I think i'd rather crush my own gasping throat
Than to face that future
Ain't you gonna cry for me gal
Aint' yo ugonna cry for me
Aint' yo ugonna cry for me gal
Ain't you gonna cry for me

aint you gonna cry aint you gonna cry
aint you gonna cry etc. etc. 

www.thosepoorbastards.com