Serenity Missing in Considering Serenity Prayer

The Serenity Prayer is short and insightful, whose opening is well known:

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.

Prostestant theologian Reinhold Niebuhr claimed to have written it, but there seems to be a significant question of whether he was right:

Now, a law librarian at Yale, using new databases of archival documents, has found newspaper clippings and a book from as far back as 1936 that quote close versions of the prayer. The quotations are from civic leaders all over the United States — a Y.W.C.A. leader in Syracuse, a public school counselor in Oklahoma City — and are always, interestingly, by women.

Some refer to the prayer as if it were a proverb, while others appear to claim it as their own poetry. None attribute the prayer to a particular source. And they never mention Reinhold Niebuhr.