In 1865, Father Abram Ryan wrote "The Conquered Banner."
No music is specified in "Allan's Lone Star Ballads, A Collection of Southern Patriotic Songs Made During Confederate Times," Francis D. Allan, 1874, and reprint.
The form and meter suggests that it may have been composed with "The March of the Men of Harlech" in mind.
First verse-

Furl that banner! for 'tis weary.
Round its staff, 'tis drooping dreary;
Furl it, fold it, it is best:
For there's not a man to wave it,
And there's not a sword to save it,
And there's no one left to lave it
In the blood which heroes gave it;
And its foes now scorn and brave it;
Furl it, hide it, let it rest.

Father Ryan's poem is perhaps the most poignant of those written following the loss of the War.
Full lyrics also at Civil War Poetry website Conquered Banner
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The song "March of the Sons of Confederate Veterans," lyrics by James F. Chumbley, commemorates the men who fought for the Confederacy. I see nothing specifically racist in its words.
The sentiments are expressed at meetings of descendants; The United Daughters of the Confederacy, Children of the Confederacy, and the Sons..., and at graveside memorials for veterans on Confederate Memorial Day (April 28 this year, a mandatory state holiday in South Carolina).
Photographs of the events in Jacksonville, FL at: Jacksonville

The song may be heard at the website of the Saluda SC chapter, Sons of Confederate Veterans: March

The 115th Annual Convention of the United Daughters of the Confederacy will be held in Richmond, Nov. 6-10.
headquarters UDC