This one is a bit of a stinker. It seems that no amount of rationalising in the moment (e.g. in a single conversation) will sway the majority of conspiracy theorists. There are of course the shepherds and sheep in the group, with some simply acting as cult leaders for their own enrichment and whom feed the cult with it's 'strictures' and 'chants' and other cult entrapments - these people will obviously not be swayed while they profit from being a prophet.As for the conspiracy-biased individuals: what to do?
The sheep will join the group and feed off it not because of the subject matter of their conspiracy theory, but for group inclusion. To feel special and more in control by knowing something special that most others can't see. Other things like emergent group behaviour, inclusion, self promotion, extremism (how many cults don't end up extreme?), hierarchical positioning, and so on will tend to amplify the nonsense. Other reasons for being a member too, but I think the above is very common.
For someone like that to accept they are completely deluded is to lose everything they used it for to make themselves feel special, to sustain themselves, to not feel overwhelmed by a complex world beyond much understanding. Human's are rarely rational, hence our need for methodologies to be able to achieve complex projects that can't work on personal opinion, bias and prejudice. So trying a rational argument is rarely effective, maybe even counter productive.
I reckon it requires a social change to overcome it. The more the mainstream media debunk conspiracies the more people will gradually drift away from them, but since many mainstream media feed from our propensity for ever more extreme content, and conspiracy stories provide the perfect topic, this seems unlikely.