How do I create generic FMEAs for family of products?

You could create a base FMEA that addresses common failures that similar products (a product family) are susceptible to.

Branches from such base FMEAs can be soft attached into specific product FMEAs as required. The specific product FMEA additionally can have its own branches too.

Any changes made to the base FMEA will reflect automatically in all FMEAs it is linked into.