Are there plausible intuitions about the ways the world works that stand as credible alternatives to Hempel's covering law model? There are. A particularly strong alternative links explanation to causation, and goes on to understand causation in terms of the real causal powers of various entities and structures. Rom Harre's work explored this approach earliest (Madden and Harre, Causal Powers: Theory of Natural Necessity), and Roy Bhaskar's theories of critical realism push these intuitions further (Critical Realism: Essential Readings (Critical Realism: Interventions)). Bhaskar and Archer's volume Critical Realism: Essential Readings (Critical Realism: Interventions) (Bhaskar, Archer, Collier, Lawson, and Norrie, eds.) is a good exposure to current controversies in this tradition. Paul Lewis's "Realism, Causality, and the Problem of Social Structure" (link) is worth reading as well.
Here the idea is that causation is not to be understood along Humean lines, as no more than constant conjunction. (This is where the insistence on general laws originates.) Instead, the idea of a causal power is taken as a starting point. Things have the capacity to bring about changes of specific circumstances, in virtue of their inner constitution (or what Harre is content to call their essences). (I would put Nancy Cartwright's ideas about causation and general laws in the same general vicinity (How the Laws of Physics Lie, Nature's Capacities and Their Measurements), though she is not a critical realist. But her critique of laws and her preference for capacities is similar.)
This doesn't mean that there is a bright line between causal powers and regularities. If a certain thing X has the power to bring about Y, then it is true that there is some generalization available along the lines of "whenever X, Y occurs." The point here is about ontological primacy: is it the power or the law that is more fundamental? And Harre, Bhaskar, and Cartwright all agree that it is the power that is basic and the thing's powers are dependent upon its real constitution.
This set of realist intuitions about causation comports very well with the theory of causal mechanisms. According to this approach, when we ask for an explanation of something, we are asking questions along these lines: what are the real embodied mechanisms that bring about a given outcome? And what is the underlying substrate that gives these mechanisms their causal force?
When causal realism is brought to the social and historical sciences, it brings the idea that there are structures, entities, and forces in the social world that really exist and that supervene upon a substrate of activity that give substance to their causal powers. In the case of the social world, that substrate is the socially constituted, socially situated actor, or what I call the premise of methodological localism.
One implication of this ontology is directional for setting a program of inquiry. Instead of looking for general laws of a given domain, the researcher is encouraged to discover the particular causal properties and powers of specific kinds of things.
This emphasis on the particular and the local is particularly well suited to the challenges of historical and social research. Nancy Cartwright doubts the validity of searching for even exact laws of physics. And this doubt is all the more reasonable in the case of social phenomena. It is pointless to look for general laws of bureaucracy, the military, or colonialism. What is more promising, however, is to examine particular configurations of institutions and settings, and to attempt to determine their causal powers in the setting of a group of social actors.
Suppose we are interested in France's collapse in the Franco-Prussian War (link). We might expend significant research work on discerning the organizational and command structure of the French Army in the 1850s and 1860s. We might look in detail at Napoleon III's state apparatus, including its international relations bureau. And we might gather information on the structure, capacity, and organization of the French rail system. Then we might offer an explanation of a numer of events that occurred in 1870 as the result of the causal properties of those historically embodied organizations and institutions. The real performance properties of the rail system under a range of initial conditions can be worked out. The conditions presented by the rapid mobilization required by suddenly looming war can be investigated. And the logistical collapse that ensued can be explained as the result of the specific causal properties of that complex system. And here is an important point: the Italian rail system at the time had some similarities and some differences. So it is a matter of empirical and theoretical investigation to arrive at an account of the causal properties of that system. We cannot simply infer from the French case to the Italian case, and of course we can't hope to find a general law of rail systems.
The point here is a fundamental one. The covering law model depends on a metaphysics that gives primacy to laws of nature. The framework of critical realism and its cousins depends on a view of the world as consisting of things and processes with real causal powers. This intellectual framework is applicable to the social world as well as to the natural world. And it provides a strong intellectual basis for postulating and investigating social causal mechanisms. Any conception of causal powers requires that we have an idea of the nature of the substrate of causation in various areas. And the social metaphysics of actor-centered sociology provide a strong candidate for such a framework in the case of social causation.