Deism was never a church, so its history is largely the history of an argument. For roughly half a century English divines answered it in print, and the answers shaped the position as much as its own advocates did.
John Toland opened the exchange with Christianity not Mysterious (1696), which argued that nothing in the gospel is above reason and that mystery is a later accretion. The book was burned in Dublin. Matthew Tindal's Christianity as Old as the Creation (1730) pressed the case to its conclusion: if God is just and wants all people saved, the terms of salvation must have been available to everyone in every age, so revelation can add nothing to what reason already supplies. It drew dozens of published replies and is often called the deist's bible, though not by deists.
The most durable answer was Joseph Butler's The Analogy of Religion (1736). Butler did not defend revelation by attacking reason. He accepted the deists' own premise, that nature is the work of the creator, and argued that nature is quite as full of difficulty, apparent injustice and unexplained arrangement as scripture is. If those features do not disqualify the book of nature, they cannot disqualify the book of revelation either. The argument was aimed precisely at readers who had already conceded the deist starting point, and it is generally held to have taken the force out of the controversy in England.
What followed was less a defeat than an absorption. The historical and textual criticism the deists had turned on scripture was taken up by scholars inside the churches and pursued further than the deists had taken it, while their positive doctrine, a creator known through nature, morality independent of revelation, passed into Unitarianism and liberal theology. Deism stopped being a party because a good deal of what it argued stopped being contested.