It sounds like the song you mean is Come Unto Me and I believe the composer is Charles P. Jones. It is based on Matthew 11:28. Not sure of the copyright date but here is the whole song. I hope this helped you.

Come Unto Me

Verse: 1
Hear the blessed Savior calling the oppressed,
oh ye heavy laden, come to me and rest,
come no longer tarry, I your load will bear,
bring me every burden, bring me every care.

Chorus:
Come unto me, I will give you rest,
take my yoke upon you, hear me and be blest,
I am meek and lowly, come and trust my might,
come my yoke is easy, and my burden light.

Verse: 2
Are you disappointed, wandering here and there,
dragging chains of doubt and loaded down with care,
do unholy feelings struggle in your breast,
bring your case to Jesus, he will give you rest.

Verse: 3
Stumbling on the mountains dark with sin and shame,
stumbling toward the pit of hell's consuming flame,
by the powers of sin deluded and oppressed,
hear the tender Shepard, come to me and rest.

Verse: 4
Have you cares of business, cares of pressing debt,
cares of social life or cares of hopes unmet,
are you by remorse or sense of guilt depressed,
come right on to Jesus, he will give you rest.

Verse: 5
Have you by temptations often conquered been,
has a sense of weakness brought distress within,
Christ will sanctify you, if you'll claim his best,
in the holy spirit he will give you rest.

I am looking for the music for a hymn that our church's choir sang when I was a boy. The words are familiar:

"Come unto me, all ye that labor and I will give you rest" (A section)

"Take my yoke upon thee" (B section)

Anyone familiar with the composer and title of this? It is in a major key and has some very nice harmony parts.