In June 1959, Morris, aged 23, wed 45-year-old Ed "Buzz" Burke, a wealthy Texas oilman from Houston, Texas. In April 1960 it was reported that the couple had a baby boy. The couple then had two more children. Her husband died, and she then remarried and had one more child. She currently has one granddaughter. As of 2010 she was still living in Texas with her husband.