I think there are a couple ways to go about answering this question. If you go about it by seeing whether people who are related and people with a few life experiences that you want to track score high on a conscientiousness test, you're not really answering the question "what training would work?"
I don't have a direct answer to that, but I do have several bits of information that would be very useful for a person who would like to try and solve this:
Dabrowski did research on morality also. His theory is that there are certain traits called &qu... (read more)
I have very slowly become a lot more conscientious over the course of my life. It feels like I made a deliberate effort to do so by eg leaning hard on calendars, todo lists and such, but it may simply be ageing.
2Douglas_Knight
Heckman and Tough just wrote a whole book claiming that there are cheap ways to increase conscientiousness of children, though probably only at the low end.
If it's worth saying, but not worth its own post, even in Discussion, it goes here.