As mentioned in the other threads the 'original' (?) composer was one Ned Straight. The dates given for both Straight and Madison/Falkenstein are a bit off though:

Lay My Head Beneath a Rose.
By Ned Straight, Composer of Josephus Orange blossom, The Colored Grenadiers, No Work, &c.

Darling, fold me to you closer,
        As you did in days of yore;
Press your lips upon my forehead,
        Ere I see the golden shore.
Life is from me fastly fleeting,
        Soon I'll be in sweet repose;
When I am gone I ask this favor,
        Lay my head beneath a rose.
                CHORUS.
Lay me where sweet flowers blossom–
        Where dainty lily grows;
Where the pink and violets mingle,
        Lay my head beneath a rose.

Darling one, when first I met you,
        When I pledged you hand and heart,
There were roses on your cheeks love,
        And we vowed we ne'er would part.
One more kiss, for I am going
        Far beyond all earthly woes;
Let my grave be like your cheeks, love,
        Covered with the blushing rose.                CHORUS.

[Marsan, Henry DE, New Comic and Sentimental Singer's Journal, No.162, Vol.II, (New York: H. DE Marsan, 1868, p.493)]

Note: Pretty much the same stuff. There are several Ned Straight mentions in newspapers &c between this and the earliest Madison/Falkenstein copyright I've found so far, 1897.

Somewhere along the line it became part of a play and we learn why he is dying. I thought it was TB but… see 1908 Arthur Tavares & Royal Hawaiian Quintette references that follow. Mostly likely fiction either way.