Here's a version attributed to Andrae Crouch (1982), but I can't believe that's the earliest version. Click here for a YouTube recording of an Andrae Crouch recording of the song from the late 1970s. I suppose it's possible that Crouch is the author - many of his compositions have a timelessness and simplicity that make them seem traditional. The Harry Fox Agency Songfile Website lists a version of this song by Crouch, but another as traditional. So, we're back to square one.

CAN'T NOBODY DO ME LIKE JESUS
(attributed to Andrae Crouch)

Chorus:
Can't nobody do me like Jesus
Can't nobody do me like the Lord
Can't nobody do me like Jesus
He's my friend
(repeat)

He healed my body, then he told me to run on (3x),
He's my friend

Chorus

He saved my soul, put my name on the roll (3x),
He's my friend

He filled me with the Holy Ghost, then he told me to run on (3x),
He's my friend

He's my friend, my friend.
I know that He's my friend, my friend

Chorus x2

I said He's my friend
I'm so glad He's my friend
He's my friend


Andrae' Crouch
© 1982 Bud-John Songs, Inc.

source: http://artists.letssingit.com/crabb-family-lyrics-cant-nobody-do-me-like-jesus-n8dvk76