Telling them that the doctrine wasn't invented until the 1830s likely won't mean much to them. They will likely say that the apostles believed in the doctrine, as evidenced by the "fact" that it is in Scripture, and the church lost the doctrine for all those centuries.
As far as ways to counter the belief to them...
I find that passages used to defend the Rapture doctrine fall into three categories: 1) passages that require a series of logical steps in order to arrive at the conclusion that it is referring to the Rapture; 2) passages that require one to already believe in the Rapture in order to see it in the text; 3) poor exegesis/poor critical reading.
1) One example is "the marriage supper of the lamb" in Revelation. Because they are in heaven, and because the next passage still describes people being on earth, and because Christ returns several chapters later, and because Revelation is clearly chronological, and because this passage is clearly literal, it therefore means that those people were caught up to heaven prior to Christ's return and this demonstrates the truth of the Rapture.
2) One example is also in Revelation, chapter 4, I believe: "Come up hither..." If one had never heard of the Rapture, one would conclude that God is going to show John a vision of heaven and future events. But because one already believes in the Rapture, one is able to insert the Rapture into that text and imagine that that passage shows the Rapture.
3) One example is Matthew 24/25 in the Olivet Discourse. "One will be taken and the other will be left." It is easy to separate that verse from the rest of the passage and conclude that during that period of tribulation there will be people taken, and imagine that they are taken to heaven. But a proper and complete reading of the text indicates that those who are taken are taken to destruction and judgement.