How do I get the mother of my deceased son's daughter to establish paternity?

Consult with an attorney. You will have to go to court. But it will depend on the level of grandparent's rights, if any, in your area.

For what legal purpose? If, as ScottGem suggests, you have rights to grandparent visitation, that might be a legitimate purpose. Or if he died intestate and you are trying to determine heirship, that might be another reason. But courts are reluctant to get involved if you want to establish paternity merely out of curiosity.