Hume is perhaps the most relentlessly empiricist, and even athiestic writer I've read in this section. Most of the Enlightenment writers can be classed as Diests and then we can argue about what that means. I don't really think that Hume can though.
Cleanthes, who is taken to represent the teleological or "Design" argument for God's existence, argues that the universe seems to operate in a way that resembles a number of machines. He says that "the curious adapting of means to ends, throughout nature" resembles the machines of human design. Therefore the universe must also be designed. Philo argues that we cannot apply the rules of one narrow corner of the universe (the mind) to the rest of the universe and hope for any homology. Moreover, no man has any experience of the origin of the universe. We do not see all design in nature, which is infinite. For all we know, the universe might consist of very shoddy workmanship! Also, we cannot claim to know the mind of the Diety. Our "limited experience" is no means by which to judge the "unlimited extent of nature". Ultimately, Philo (and Hume) argues that the (intelligent) design argument "exceeds all human reason and inquiry".
Demea makes the cosmological argument, or the argument from first cause. Matter could not have acquired motion without a first mover. Philo asks why this must be the case. Humans have no experience of matter at absolute rest anywhere in the universe. Demea argues that "whatever exists must have a cause or reason of its existence." Philo asks why this must be so, and if there must also be a cause for the mind of God. Also, if we can ever account for every fact in the chain of facts, why would we need to account for the collection of facts? Ultimately, he scandalizes Demea by discussing the problem of evil, specifically how it came into being.
Finally, Philo claims to undermine religion at every turn in order to reform belief. "When religion stood entirely upon temper and education, it was thought proper to encourage melancholy; as indeed mankind never have recourse to superior powers so readily as in that condition. But as men have now learned to form principles and to draw consequences, it is necessary to change the batteries, and to make use of such arguments as will endure at least some scrutiny and examination." Ultimately, though Philo, and Hume, do not admit of any religious arguments that can endure scrutiny.