His name WAS John Newton, but he didn't sing it on a slave ship. He wrote it in 1772, many years after he had turned to God during that storm (1748), abandoned the slave trade(1754) and become a clergyman (1764).

"Several retellings of Newton's life story claim that he was carrying slaves during the voyage in which he experienced his conversion, but the ship was carrying livestock, wood, and beeswax from the coast of Africa. (Aitken, p. 76.)

While aboard the ship Greyhound, Newton gained notoriety for being one of the most profane men the captain had ever met. In a culture where sailors commonly used oaths and swore, Newton was admonished several times for not only using the worst words the captain had ever heard, but creating new ones to exceed the limits of verbal debauchery.[11] In March 1748, while the Greyhound was in the North Atlantic, a violent storm came upon the ship that was so rough it swept overboard a crew member who was standing where Newton had been moments before.[d] After hours of the crew emptying water from the ship and expecting to be capsized, Newton and another mate tied themselves to the ship's pump to keep from being washed overboard, working for several hours.[12] After proposing the measure to the captain, Newton had turned and said, "If this will not do, then Lord have mercy upon us!"[13][14] Newton rested briefly before returning to the deck to steer for the next eleven hours. During his time at the wheel he pondered his divine challenge.[12]

About two weeks later, the battered ship and starving crew landed in Lough Swilly, Ireland. For several weeks before the storm, Newton had been reading The Christian's Pattern, a summary of the 15th-century The Imitation of Christ by Thomas à Kempis. The memory of the uttered phrase in a moment of desperation did not leave him; he began to ask if he was worthy of God's mercy or in any way redeemable as he had not only neglected his faith but directly opposed it, mocking others who showed theirs, deriding and denouncing God as a myth. He came to believe that God had sent him a profound message and had begun to work through him.[15]" - Wikipedia