Here's the John Jacob Niles recording. It's very different from the melody Christy Moore uses. I much prefer the plainer melody used by Christy Moore.
https://www.youtube.com/watch?v=h_yA5l9Vghg

Here is the Traditional Ballad Index entry on the song.

Black Is the Color

DESCRIPTION: "(Black, black,) black is the color of my true love's hair...." The singer describes the beautiful girl he is in love with. (He regretfully concedes that they will never be married)
AUTHOR: unknown (see NOTES)
EARLIEST DATE: 1916 (Cecil Sharp collection)
KEYWORDS: love courting hair beauty separation nonballad
FOUND IN: US(Ap,SE,So)
REFERENCES (10 citations):
Lomax/Lomax-FolkSongUSA 16, "Black Is the Color" (1 text, 1 tune)
Lomax- FSNA 100, "Black Is the Color" (1 text, 1 tune)
Ritchie-FolkSongsOfTheSouthernAppalachians, p. 88, "Black is the Color" (1 text, 1 tune, with several floating lines including some that appear to be from "Lady Mary Anne" or something related)
Sharp-EnglishFolkSongsFromSouthernAppalachians 85, "Black is the Colour" (1 text, 1 tune)
Sharp/Karpeles-EightyEnglishFolkSongs 41, "Black is the Colour" (1 text, 1 tune)
Burton/Manning-EastTennesseeStateCollectionVol1, p. 107, "Black Is the Color of My True Love's Hair" (1 text, 1 tune)
Darling-NewAmericanSongster, pp. 267-268, "Black is the Color" (1 text)
Silber/Silber-FolksingersWordbook, p. 145, "Black Is The Color" (1 text)
SongsOfAllTime, p.17, "Black Is the Color" (1 text, 1 tune)
DT, BLACKCOL* BLACKCO2*
Roud #3103
RECORDINGS:
Dellie Norton, "Black is the Colour" (on OldTrad1, FsrMtns4)
Pete Seeger, "Black is the Color" (on PeteSeeger18)
NOTES [54 words]: John Jacob Niles, who is largely responsible for popularizing this song, also claims to have written it. For a recently composed song, however, it exists in unusually diverse and widespread forms. Randolph notes connections with English pieces, and Lomax correctly observes that the tune resembles "Fair and Tender Ladies." - RBW
Last updated in version 6.3
File: LxU016

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The Ballad Index Copyright 2022 by Robert B. Waltz and David G. Engle.

I think we can reasonably conclude that the song is in the public domain, although Niles's operatic melody may be under copyright. See our DTStudy thread for various versions of the song.