Generations of recovering alcoholics, soldiers, weary parents, exploited workers and just about anybody feeling beaten down by life have found solace in a short prayer that begins, “God grant me the serenity to accept the things I cannot change.†Now the Serenity Prayer is about to endure a controversy over its authorship that is likely to be anything but serene. For more than 70 years, the composer of the prayer was thought to be the Protestant theologian Reinhold Niebuhr, one of modern Christianity’s towering figures. Niebuhr, who died in 1971, said he was quite sure he had written it, and...