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 (320003@1)          C (x32010@1)(Cadd9)  G (320003@1)    D (xx0232@1)      
I believe submarines
G (320003@1)          C (x32010@1)(Cadd9)  G (320003@1)     D (xx0232@1)
Underneath deep blue seas
G (320003@1)          C (x32010@1)(Cadd9)  G (320003@1)     D (xx0232@1)
Saw the flags: Japanese
G (320003@1)           C (x32010@1)(Cadd9)  G (320003@1)     D (xx0232@1)
No one will believe me

Bridge

Em (022000@1)                   D (xx0232@1)Ran back to the town bar and
GI (320003@1)told the people how
Em (022000@1)                    DI (xx0232@1)had seen the submarine and
CEveryone (x32010@1)laughed aloud

G (320003@1)  C (x32010@1)Cadd9 (x32030@1)G (320003@1)    D (xx0232@1)
G (320003@1)  C (x32010@1)Cadd9 (x32030@1)G (320003@1)     D (xx0232@1)G (320003@1)          C (x32010@1)(Cadd9)  G (320003@1)    D (xx0232@1)
I did spy periscopes
G (320003@1)          C (x32010@1)(Cadd9)  G (320003@1)    D (xx0232@1)
Dead of night on the eastern coast
G (320003@1)          C (x32010@1)(Cadd9)  G (320003@1)    D (xx0232@1)
The police made them jokes
G (320003@1)          C (x32010@1)(Cadd9)  G (320003@1)    D (xx0232@1)
Told me I'd seen a ghost

Em (022000@1)                 D (xx0232@1)                  GEveryone (320003@1)thinks I'm a liar  No one knows the truth
Em (022000@1)                 D (xx0232@1)                   CIf (x32010@1)it was a bigger fire I would be on the roof

G (320003@1)          C (x32010@1)(Cadd9)  Em (022000@1)   D (xx0232@1)
G (320003@1)          C (x32010@1)(Cadd9)  Em (022000@1)   D (xx0232@1)
G (320003@1)          C (x32010@1)(Cadd9)  G (320003@1)    D (xx0232@1)
G (320003@1)          C (x32010@1)(Cadd9)  G (320003@1)    D (xx0232@1)G (320003@1)          C (x32010@1)(Cadd9)  Em (022000@1)   D (xx0232@1)
Ships will rust in Baldwin Bay (Let me go!)
G (320003@1)          C (x32010@1)(Cadd9)  Em (022000@1)   D (xx0232@1)
No one trusts what I say (I don't know!)
G (320003@1)          C (x32010@1)(Cadd9)  Em (022000@1)   D (xx0232@1)
Oh my God, no one paid  (Attention!)
G (320003@1)          C (x32010@1)(Cadd9)  Em (022000@1)   D (xx0232@1)
Overnight my hair turned gray  (Oh oh oh!)

Em (022000@1)                          D (xx0232@1)                   GIn (320003@1)the end it boils down to credibility
Em (022000@1)                          D (xx0232@1)                        CI (x32010@1)had none, so I will die with the secrets of the sea

G (320003@1)          C (x32010@1)(Cadd9)  Em (022000@1)   D (xx0232@1)
G (320003@1)          C (x32010@1)(Cadd9)  Em (022000@1)   D (xx0232@1)Then this chord progression for the rest of it with the rests.

G (320003@1)          C (x32010@1)(Cadd9)  G (320003@1)    D (xx0232@1)
(Submarine! Can't find me! Submarine!)

Submarine...

(Submarine!)