Only one hymn by Alice Jean Cleator in the Cyberhymnal, published in 1903.
All I can find is one of those Google 'translations' from a Japanese blog website.
Peace, the Mormon children's songbook I think you saw has a number of songs by non-Mormons. She wrote several religious songs for children including "Be a Little Sunbeam," on the Website of the Woman's Missionary Union, an auxiliary to the Southern Baptist Convention.

Masato, it may be in one of the song books in the list of Universalist Song and hymn books. See the annotated bibliography. Item 100, Colgrove, 1912, "Lessons from Nature's Voices," is a Sunday school songbook that contains 60 songs based on Nature, including at least one by Cleator.
www.sksm.edu/research/papers/bibliography.pdf