I have a very small collection of very old music classroom song books here at school:
Song-Land for Early Grades, Forty-three Sing-songs by Paul Bliss. No date given, but the inscription inside the cover reads 1932
The Progressive Music Series (for Basal Use) Silver Burdett and Co 1914 this still is a very popular publisher of music series. Very definitely a contender in your quest!
Introductory Music, Music Education Series, Ginn and Co, 1923 (Ginn has now merged with Silver Burdett!)

I hope these have helped you. I think I have a few others at home which I will check tonight.All of the ones listed here have the Keene NH School District stamp inside the cover, which tells me they were used here in the smallest city in Cow Hampshire. Why not in a one-room schoolhouse in Colorado?