FORTRAN source code for a program that computes all elastic constants when you give it any two independent ones.
It will do wave speeds if you give it density.
It will also estimate degraded stiffness from porosity or cracking if you give it some additional information about the nature of the damage.
You may download the rest of the document here. This download includes a help file.
You might also find the following table of relationships between elastic constants to be more detailed than similar tables available in most elasticity books: