This is a long shot BUT I found a JOSEPH F MURRAY on the Social Security Death Index - date of birth is Jan. 21, 1928 - date of death is May 21, 2011. His Social Security card was issued in Louisiana, and the place of his last residence is Pearland, Brazoria, Texas.
On Ancestry.com I found an obituary for this JOSEPH F MURRAY - I will transcribe it below:
FRIENDSHIP, TEXAS - JOSEPH FRANK MURRAY, JR., age 83, died Saturday May 21, 2011 in the Memorial Herman Hospital, Houston. He is survived by his life long companion, the late RUTH J ANGELO, and is survived by her 2 children, EDDIE ANGELO and JOY ANGELO BUSCH. Friends will be received May 28 from 8 - 11 a.m. at the Funeral Home Chapel Service at Harry McNeely & Son, in Hammond. Interment will follow at the Parklawn Memorial Gardens, Hammond.
I thought there may be a chance that this is your JOSEPH FRANCIS MURRAY - "FRANK" is often a nickname for "FRANCIS" and the birth date is only off by 1 day.
Since this JOSEPH F MURRAY's social security number was issued in Louisiana, I looked on the 1940 Census - I found a "MURRAY" family living at 2320 N. Derbigny in New Orleans, Lousiana. The head of the household is JOSEPH F MURRAY, SR., age 43; his wife is JULIA MURRAY, age 39; and their son is JOSEPH F MURRAY, age 12.
I hope this is the JOSEPH FRANCIS MURRAY you are looking for!