Well, it's a tough one. From Ancestry . com:
Name: Howard Thomas Byrne
SSN: 107-20-7051
Last Residence: 90808 Long Beach, Los Angeles, California, United States of America
Born: 29 Oct 1927
Died: 13 Feb 2010
State (Year) SSN issued: New York (Before
Name: Gloria Carmel Byrne
SSN: 072-22-9349
Last Residence: 90808 Long Beach, Los Angeles, California, United States of America
Born: 12 Jul 1928
Last Benefit: 90808 Long Beach, Los Angeles, California, United States of America
Died: 13 Nov 2008
State (Year) SSN issued: New York (Before 1951)
That information and $16 (each) will get you a "Computer Extract of Social Security Card Application" (or, for $27, a photocopy of the actual application). The records should include the place of birth as well as parent's names.
http://www.socialsecurity.gov/foia/html/foia_guide.htm