I finally sent in a form to purchase a copy of my Grandmother's birth record. Arkansas started keeping birth records in 1914. Gramma was born 1911, so I assumed they would have a "delayed" birth certificate. No such luck. I'm assuming in the 1970's when someone applied for Social Security benefits, they didn't have to show a birth certificate. Times have changed. Today, we do need a certified birth certificate.
The Social Security Death Index does show Gramma's birth date and I do have a copy of Gramma's Social Security card application. This will have to do for a birth date and location until I can think of another record.