There are many different Enlightenment philosophers, so I will restrict myself to just two. Also, I will list sources as you are asking, but I will also provide brief summaries.

David Hume (Scottish Enlightenment, lived from 1711 to 1776):

Hume believed that any action is free when it is caused by the agent. He believed we are responsible for any free action, and so he believed that moral responsibility is compatible with determinism (namely, the view, put roughly, that every event is caused by a preceding event, such that no agent can spontaneously "initiate" a new series of events). Since Hume thinks that any agent-caused action is free, it never bothers him that the very decision an agent makes to cause an action is itself caused by something prior to it. Hume's view that freedom and moral responsibility are compatible with determinism is the perfect example of philosophical "compatiblism."

Primary sources:

“Of liberty and necessity” in A Treatise of Human Nature (2.3.1–2)

“Of liberty and necessity” in Enquiry concerning Human Understanding (sec. 8).

Secondary sources:

Penelhum, Terence. 2000. Themes in Hume: The Self, the Will, Religion, Oxford: Clarendon Press.

Harris, James, 2005. Of Liberty and Necessity: The Free Will Debate in Eighteenth-Century British Philosophy, Oxford: Clarendon.

Fields, Lloyd, 1988. “Hume on Responsibility,” Hume Studies, 14: 161–75.

Gottfried Wilhelm Leibniz (German Enlightenment, lived from 1646 to 1716):

Leibniz is also a compatibilism. He believes that an action is free insofar as it spontaneously flowed from a person's own individual nature and insofar as it represented the choice of what one perceived to be the best option at the time. I could have chosen to own ten dogs, and so there is some possible "world" in which I did decide to own ten dogs. But not in this world. Why not? Well, that's because God decided to create this world -- in which I decided to own only one dog. For this reason, every possibility that is compatible with my still being me (e.g., possibilities like my owning ten dogs, my owning ten cats, versus possibilities like my being a salmon instead of a human being) exists in some possible world that God decided not to create, for the sake of choosing this one instead. The fact that it was up to God doesn't negate the fact that I am free and responsible for my actions because they flow from my own nature and conception of what's good.

Primary source:

On Contingency

Secondary sources:

Curley, Edwin, 1972. “The Root of Contingency,” In Harry G. Frankfurt ( ed.), Leibniz: A Collection of Critical Essays, New York: Doubleday, pp. 69–97.

Adams, Robert Merrihew, 1994 Leibniz: Determinist, Theist, Idealist, Oxford: Oxford University Press.