The Carter Family recorded this song in 1936, the same year as the W. Madison (words) G. Falkenstein (music) sheet music was issued. The Carter lyrics are close to those of the sheet music (see Vissjoy post above) but there is no refrain.

Carter version

Darling, clasp me to your bosom
As you did in days of yore
Lay your hand upon my forehead
Ere I reach the golden shore.

Life from me is fastly falling
Soon I'll be in sweet repose
When I'm gone I ask this favor
Lay my head beneath the rose.

Darling, first you said you loved me
When you gave me hand and heart
There were roses on your cheeks, love
As we vowed we ne'er would part.

One more kiss for I am going
Far beyond all earthly woe
May your life be like your cheeks, love
Covered with the blossomed rose.

He has crossed the shadowed valley
Where the living waters flow
Love has answered all his pleading
And he sleeps in sweet repose.

Beneath a grassy mound he's resting
Where the golden sunset glows
Love has answered all his pleading
And he sleeps in sweet repose.

Recorded 6/9/36, NYC.
http://www.icdc.com/~fmoore/carterfamily/lay_my_head_beneath_the_rose.htm
Lay My Head

Lyrics are identical at www.silcom.com/~peterf/ideas/carter4.htm#lees,   but an instrumental break is indicated after 2nd and 4th verses.
Lyrics also identical at http://bluegrasslyrics.com/carter_song.cfm-recordID=c119.htm

Decca 46005 issued October 1946, may be heard at Honking Duck

MP3 at Lay My Head
Also recorded by Hank Snow.