Ukuleles come in a variation of tuning, the most common of which is GCEA, G being the third highest of 
the four. In order to play "Keep the Car Running", the C string must be tuned to a B, which is one 
fret/half tone down. This can be achieved by tuning the fifth fret on the C string to the open 
E string.

In this tuning, the chords are as follows:
D5: 2350 (ADAA)
Gadd9: 0335 (GDGD);
alternatively, you can play this chord as Gadd9/B: 0035 (GBGD)
Asus4: 2300 (ADEA)
D5/C#: 2250 (AC#AA)
D5/B: 2050 (GBEA)
G: 0332 (GDGB)

If, for one reason or another, you would like to play the song in standard (GCEA) tuning, here are the 
chords:
D5: 2250 (ADAA)
Gadd9: 0235 (GDGD);
alternatively, you can play this chord as Gadd9/B: 0035 (GBGD)
Asus4: 2200 (ADEA)
D5/C#: 2150 (AC#AA)
D5/B: 2(-1)50 (GBEA)
unless you possess some ungodly fretboard which allows you go to lower than the open string, this chord 
is impossible :) Maybe just play it as 2x50, muting the C string.
G: 0232 (GDGB)

Intro is a strum/picking variation of D5

D5
Every night my dream's the same
Same old city with a different name
Gadd9
Men are coming to take me away
D5
Don't know why but I know I can't stay


Verse:
D5
There's a weight that's pressing down

Late at night I can hear the sound
Gadd9
Even the noise you make when you sleep
D5
Can't swim across the river so deep


Chorus:
Asus4                      D
They know my name 'cause I told it to them
         B                    D5                 
But they don't know where and they don't know when
                                D5
It's coming, when it's coming


Verse:
D5
There's a fear I get so deep
Knew the sentence before I could speak
Gadd9            D5
Ohh Ohh Ohh Ohhh


Chorus:
Asus4                      D
They know my name 'cause I told it to them
         B                    D5
But they don't know where and they don't know when
     Gadd9         D5             Gadd9
It's coming, or where but it's coming  
             D5 (Goes into Bridge/Intro part)
Keep the car running


Bridge/Intro (repeat as necessary): (D5)

Verse
D5
If some night I don't come home

Please don't think I've left you alone
    Gadd9
The same place animals go when they die
D5
Can't climb across a mountain so high
    Gadd9
The same city where I go when I sleep
D5
Can't swim across a river so deep


Chorus and Outro:
Asus4                      D
They know my name 'cause I told it to them
         B                    D5
But they don't know where and they don't know when
     Gadd9         D5             Gadd9
It's coming, oh when is it coming  
             D5
Keep the car running
             D5       Gadd9
Keep the car running
             D5       Gadd9
Keep the car running
             D5
Keep the car running