The second mishnah in Rosh HaShanah says that "all the people of the world" are judged on Rosh HaShanah. How should non-Jews observe the Day of Judgment?
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The nearest answer I can find refers to the prayers that Noahides can say on or before Rosh Hashonoh from “asknoah.org”
The suggested prayers contain a section from “Unesaneh Tokef”, “V’Khol Ma’aminin”, Psalm 24, and some prayers from from the booklet "Prayers, Blessings, Principles of Faith, and Divine Service for Noahides (5th Edition, pub. 20’13 by Ask Noah International)"
I saw an article where Rabbi Israel Chait addresses your question for Bnei Noach. I thought you might like his comments.