Over to you Haggis. It was indeed The Green Mile.
Shawshank was soooo close, because the same writer wrote both the original stories of Shawshank Redemption and The Green Mile (Stephen King) and the same man directed both of them too (Frank Darabont).
The quotes I only gave sections of were:
“On the day of my judgment, when I stand before God, and He asks me why did I kill one of his true miracles, what am I gonna say? That it was my job? My job?”
and
"John Coffey, just like the drink, only not spelled the same."
(RIP Michael Clark Duncan. Nobody else could have ever played the role of John Coffey.)