The Serenity Prayer, it turns out, has multiple versions. On the Alcoholics Anonymous website you’ll find the version I quoted before, though the site adds that the first person is often pluralized, “I” to “we”:

God, grant me the serenity to accept the things I cannot change,
The courage to change the things I can,
And the wisdom to know the difference.

However, Reinhold Niebuhr’s daughter Elisabeth Sifton in her memoir gives us a different version. She says that Niebuhr’s original version of the prayer was composed in 1943, was first preached by him in a Sunday sermon that year in Heath, Massachusetts, and looked like this:

God, give us grace to accept with serenity the things that cannot be changed, courage to change the things that should be changed, and the wisdom to distinguish the one from the other.

As Sifton notes on pp292-3, there are at least two major differences between these two versions. The first refers to grace and the second does not; the first refers to changing what I or we can change, the second to what should be changed. Sifton prefers the second; she says that AA “simplified” the text and her father “minded” the change but did not object.