The trick to this song is staying on top of the triplets when you're strumming. 
Some of the chords are transitions so listen for the changes.  On the C-Cadd9 
change, you just drop your pinky down right before the second G. 

Be careful towards the end of the song the chord progressions changes to include an Em 
I have chorded the whole song and it should be right.  

Enjoy. 

G            C  (Cadd9)  G      D        
I believe submarines
G            C  (Cadd9)  G       D  
Underneath deep blue seas
G            C  (Cadd9)  G       D  
Saw the flags: Japanese
G             C  (Cadd9)  G       D  
No one will believe me

Bridge 

Em                     D 
Ran back to the town bar and
G
I told the people how
Em                      D
I had seen the submarine and
C
Everyone laughed aloud 

G    C  Cadd9  G      D  
G    C  Cadd9  G       D  

G            C  (Cadd9)  G      D  
I did spy periscopes
G            C  (Cadd9)  G      D  
Dead of night on the eastern coast
G            C  (Cadd9)  G      D  
The police made them jokes
G            C  (Cadd9)  G      D  
Told me I'd seen a ghost

Em                   D                    G
Everyone thinks I'm a liar  No one knows the truth
Em                   D                     C
If it was a bigger fire I would be on the roof

G            C  (Cadd9)  Em     D  
G            C  (Cadd9)  Em     D  
G            C  (Cadd9)  G      D  
G            C  (Cadd9)  G      D  

G            C  (Cadd9)  Em     D  
Ships will rust in Baldwin Bay (Let me go!)
G            C  (Cadd9)  Em     D  
No one trusts what I say (I don't know!)
G            C  (Cadd9)  Em     D  
Oh my God, no one paid  (Attention!)
G            C  (Cadd9)  Em     D  
Overnight my hair turned gray  (Oh oh oh!)

Em                            D                     G
In the end it boils down to credibility
Em                            D                          C
I had none, so I will die with the secrets of the sea

G            C  (Cadd9)  Em     D  
G            C  (Cadd9)  Em     D  

Then this chord progression for the rest of it with the rests. 

G            C  (Cadd9)  G      D  
(Submarine! Can't find me! Submarine!)

Submarine...

(Submarine!)