Is it actually possible to use generics when defining mappings in Orika?

It is possible, you need to use the MapperFactory#classMap(Type<A>, Type<B>) API instead of MapperFactory#classMap(Class<A>, Class<B>).

You can find a lot of examples in Orika tests in the generics package.

To construct a Type instance you can use an in-place anonymous subclass of TypeBuilder:

Type<MyGenericClass<GenericParam1, GenericParam2>> type =
    new TypeBuilder<MyGenericClass<GenericParam1, GenericParam2>>() {}.build();

Note the brackets {} after the constructor which create the anonymous subclass. That way Orika can find out the actual MyGenericClass<GenericParam1, GenericParam2> type parameter using ((ParameterizedType) getClass().getGenericSuperclass()).getActualTypeArguments().