The whole song is one chord progression. Listen to the song to get it down. It's two counts of A, two of F#m, one of D, one of E, and two more counts of A. It's very easy and it's a beautiful song.
A
When the night has come
F#m
And the land is dark
D E A
And the moon is the only light we'll see
No I won't be afraid no I won't be afraid
Just as long as you stand stand by me
And darlin' darlin' stand by me oh now now stand by me
Stand by me stand by me
If the sky that we look upon
Should tumble and fall
And the mountains should crumble to the sea
I won't cry I won't cry no I won't shed a tear
Just as long as you stand stand by me
And darlin' darlin' stand by me oh stand by me
Stand by me stand by me stand by me-e yeah
Whenever you're in trouble won't you stand by me oh now now stand by me
Oh stand by me stand by me stand by me
Darlin' darlin' stand by me-e stand by me
Oh stand by me stand by me stand by me