"Black is the Color" is a traditional Appalachian folk song of Scottish origin. The original tune of "Black is the Color" was collected by English composer and folk song archivist Cecil Sharp. The tune that is best known today is that assigned to the traditional lyrics by John Jacob Niles. He describes how he came about to write this tune:
"'Black is The Color of My True Love's Hair'...was composed between 1916 and 1921. I had come home from eastern Kentucky, singing this song to an entirely different tune--a tune not unlike the public-domain material employed even today. My father liked the lyrics, but thought the tune was downright terrible. So I wrote myself a new tune, ending it in a nice modal manner. My composition has since been 'discovered' by many an aspiring folk-singer."
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Okay. The important part of all that palaver is that Niles wrote his version between 1916 and 1921.

The Public Domain info site says "Any Song or Musical Work Published in 1926 or Earlier is in the Public Domain in the USA." I believe this gives a definite answer. The song is now PD.