In Google Books, you can see KEEP ON THE SUNNY SIDE OF LIFE as is appeared in several old hymnals:

The Epworth Hymnal, No. 3, edited by J. M. Black (Cincinnati: Jennings & Pye, 1900), hymn #102.

The New Century Hymnal, edited by Will L. Thompson (East Liverpool, Ohio: Will L. Thompson, 1904), hymn #116.

Songs of Faith and Hope, edited by James M. Black (New York: Eaton and Mains, 1905), hymn #89.

They all say words by Ada Blenkhorn, music by J. Howard Entwisle. The oldest says "©1899 by J. Howard Entwisle."