David Hume, of course, did not think of himself as a Stoic. Traditionally, a strong concept of God or Natural Law is central to Stoic philosophy, and Hume had neither. Moreover, Hume famously declared that reason ought to be "the slave of passion", which at least superficially seems to be a direct contradiction of Stoic thought. Now, a Stoic who wanted to reclaim Hume (in the same way that every single Greek philosopher ever tried to recruit Socrates' ghost to his cause) might argue that you could construct a secular Stoicism, and that Hume defined 'reason' and 'passion' in a different way to the Stoics. I'm tempted to do that myself.
However, first I want to call attention to an area where Hume seems at least to empathize with Stoic thought. In his essay 'Delicacy of Taste and Delicacy of Passion', he says this:
SOME People are subject to a certain delicacy of passion, which makes them extremely sensible to all the accidents of life, and gives them a lively joy upon every prosperous event, as well as a piercing grief, when they meet with misfortunes and adversity. Favours and good offices easily engage their friendship; while the smallest injury provokes their resentment. Any honour or mark of distinction elevates them above measure; but they are as sensibly touched with contempt. People of this character have, no doubt, more lively enjoyments, as well as more pungent sorrows, than men of cool and sedate tempers: But, I believe, when every thing is balanced, there is no one, who would not rather be of the latter character, were he entirely master of his own disposition. Good or ill fortune is very little at our disposal: And when a person, that has this sensibility of temper, meets with any misfortune, his sorrow or resentment takes entire possession of him, and deprives him of all relish in the common occurrences of life; the right enjoyment of which forms the chief part of our happiness. Great pleasures are much less frequent than great pains; so that a sensible temper must meet with fewer trials in the former way than in the latter. Not to mention, that men of such lively passions are apt to be transported beyond all bounds of prudence and discretion, and to take false steps in the conduct of life, which are often irretrievable.
Compared to many other philosophers, Hume is an absolute pleasure to read, but for those who can't be bothered wading through the italicized paragraph, he says something like this: some people are prone to great happiness and great sadness, reacting to small good events with ecstasy and small setbacks with despair, but this isn't a good way to live. The kind of person he's talking about is the ultimate non-Stoic: somebody who's enormously and constantly affected by outside events. Hume shares the Stoic judgement on such a person, claiming that it's better to be of "cool and sedate temper". Why does he say this? Well, his two main points are thus:
1) "Good or ill fortune is very little at our disposal", so a person of strong passion basically lives with a sword over their head.
2) "Great pleasures are much less frequent than great pains", so a person of strong passion is going to be unhappy more often than not.
I contend that the whole practical element of Stoic thought can be spun out from these two points, if you grant the further assumption that we can control our passions. Unfortunately, Hume doesn't immediately grant that assumption (or at least appears not to in his other essays.) If you disagree with Hume here and think that we are "masters of [our] own disposition", then Stoicism might be for you!