If Ronny was formally adopted around 1940 - so not at birth - then there should be two versions of his birth certificate: the original one with his birth name, and a later one with his adoptive name and adoptive parents on it.
Texas allows an adoptee who has reached adulthood (defined as over 18 for this), to get a copy of their pre-adoption birth certificate simply by mailing a request and paying the processing fee. Since it only costs $10 I'd say it's worth a shot!
Instructions: adoptee's pre-adoption birth certificate in the State of Texas
Application form: adoptee's pre-adoption birth certificate in the State of Texas
I'd include a very short note saying something like:
Dear Sirs,
My father, Ronny Ross, was an adoptee and since he is deceased I am applying as his next of kin for his original birth certificate. All the necessary documents are enclosed providing the evidence you will need of his name, his decease, my relationship as next of kin (his son), and my photo ID.
It just helps to spell it all out. Do enclose copies of those documents with the form: your birth certificate, your photo ID, Ronny's death certificate. (If you have it, you can also add Ronny's adoptive birth certificate.)
Very best of luck!