You could try seeing if she had a WILL if so that might provide some info for you. If your library has a microfilm machine you ask for a inter-library loan. At some point I will be requesting the microfilm for WILLS at my library I can see if there is something there for you with your grandmother's name.
You can apply one line for a cert of death since you are her granddaughter but I suggest you mail in your request since they will provide but the cert of death and med cert of death with the completed mail in form but you only get the cert of death when you apply on line. Both forms will provide more info and its only $22.
If you know the name of the funeral home they often know the names of parents, you shouldn't have too many problems since you are the granddaughter. The funeral home collects this info because they send the death info to the register so any info they have would be the same that is on the cert of death. The obit should provide you with the funeral home.