I am trying to identify the name of a song likely popular in the 30's
or 40's. Also I need to know where I might locate a recording of it. I
only know a few lyrics:  "There's an old and faded picture on the
wall.  It's a picture of my mother and I know there is no other than
the old and faded picture on the wall."

Hello Pamjane,

The song you have in mind is Picture on the Wall.

Picture On The Wall
Version: Carter Family
Author: na
  
?There's an old and faded picture on the wall
That has been a hanging there for many years
It's a picture my mother 
For I know there is no other
That can take the place of mother on the wall

   On the wall (on the wall) on the wall (on the wall)
   How I love that dear old picture on the wall
   Time is swiftly passing by
   And I bow my head and cry
   Cause I know I'll see my mother after all

Yes the children all have gathered all have gone
And I have a little family of my own
And I know I love them well
More than any tongue can tell
But I'll hold that dear old picture on the wall

Since I lost that dear old mother years ago
There is none to which with troubles I can go
As my guitar makes its chords
I am praying to the Lord
Let me hold that dear old picture on the wall.?

Lyrics provided courtesy of Bluegrass Lyrics.Com
http://bluegrasslyrics.com/carter_song.cfm-recordID=c175.htm

Lyrics
http://www.icdc.com/~fmoore/carterfamily/picture_on_the_wall.htm
 
Read about the Carter Family here:
http://www.slipcue.com/music/country/countryartists/carterfamily.html

You will find a complete collection of the words to the songs as
recorded by the Carter Family from 1927 to 1941 here:
http://www.silcom.com/~peterf/ideas/carter.htm


The song Picture on the Wall is available at Amazon 

The Carter Family: 1927-1934 
Carter Family
Disc: 3: Track 24. Picture on the Wall

Purchase here:
http://www.amazon.com/exec/obidos/ASIN/B00005TPB7/qid=1089445194/sr=2-1/ref=sr_2_1/002-1715204-4450412


Variants

Picture on The Wall 
As sung by Ollie Gilbert, Mountain View, Arkansas on June 25, 1969
http://www.smsu.edu/folksong/maxhunter/0779/index.html
Listen to the recording here:
http://www.smsu.edu/folksong/maxhunter/0779/0779.ram


Picture on the Wall 
As sung by Glenda Sue Richardson, Mountain View, Arkansas on August 31, 1971
http://www.smsu.edu/folksong/maxhunter/1214/index.html
Listen to the recording here:
http://www.smsu.edu/folksong/maxhunter/1214/1214.ram


Search criteria:
"old and faded" "picture on the wall"
Carter Family 


I hope you find this helpful!

Best regards,
Bobbie7

Thank you so much for the information.  My father will be so pleased
when I play the song for him. :-)