Dealing with the Eternalist first; part of the problem comes from the sloppy use of language when we refer to "good" and "bad" karma. This is not in accord with the Pali which classifies volitional action as "kusala" and "akusala", skilful or unskilful. That puts a whole different slant on things. There is no one to judge your actions as good or bad; they are just inherently skilful or not. It is a mistake to think of karma as some kind of cosmic or divine law-code. It is a law, of a sort, but more akin to the Law of Gravity than the Criminal Code. It is best to think of karma as an unfolding of natural law.
This then raises the objection from the Annihilationist; where is the mechanism for this law? He cannot accept that an action done today may have effects years hence, evcn in a subsequent life-time. This objection comes from a deep-seated materialist bias. Given the assumptions of materialism, then it is insurmountable. But abandon those assumptions and it melts away like dew.
Materialism has been the dominant paradigm of science for at least two centuries. It assumes that matter is the only ontological Real. Mind is considered nothing more than a process of physical interactions.
This is a strange hypothesis, one held by many with dogmatic fervour. It is strange because if you consider the case, it is obvious that the only thing we ever really know or experience directly is our own minds. The material world we access only through our sense doors and the light of consciousness. Materialism denies what is immediately known, and gives exclusive reality only to that which is inferred.
The Buddha was certainly not a materialist, a view which he specifically denounced. He also said that Mind is the forerunner; i.e. Mind is the primary Real.
Given that assumption it is not hard to see how karma works. In the abhidhamma, karma is explained in terms of balancing voltional and resultant mind-moments. For every skilful moment of volition there will be a profitable resultant experienced as sense-impression at some later time.
Given that Mind is primary, if the material universe needs to adjust itself to accomodate these mind-moments, then it does so. We make the world with our minds.
This is not an issue peripheral to the Buddhist Path either. The most common formulation of Right View is as follows;
There is what is given, what is offered, what is sacrificed. There are fruits & results of good & bad actions. There is this world & the next world. There is mother & father. There are spontaneously reborn beings; there are priests & contemplatives who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.Right View, remember, is the first of the Path Factors. I think the Buddha gave this doctrine such central importance precisely because the proper understanding of karma (and rebirth) is essential to find the Middle Ground of the Dependent Origination and to gain freedom from the shackles of the Wrong Views. If one is stuck in either Eternalism or Materialism (Annihilationism) one simply cannot correctly apprehend the void nature of the dhammas and escape from suffering.