Conscientiousness is fairly rigid; it is, however, about as hereditable as IQ or less, from the 2 studies I have on hand:

• "Genetic and environmental effects on openness to experience, agreeableness, and conscientiousness: An adoption/twin study", Bergeman et al 1993: 29% of variance
• "Heritability of the Big Five Personality Dimensions and Their Facets: A Twin Study", Jang et al 1996: 44%

Good question. I assume you ask because conscientiousness is highly correlated with a number of positive life outcomes?

1. Conscientiousness is temporally stable, that is, in the average individual, it does not much change over time.
2. Conscientiousness is linked to a number of other personality traits - e.g. self-regulation, perseverance, etc.... These traits can be trained; and according to a quick skim of the study below, training those traits in turn effects conscientiousness, at least in children.

http://www.sas.upenn.edu/~duckwort/images/publications/EisenbergDuckworth_ConscientiousnessOriginsinChildhood_2012.pdf

1. In adults, the trait is more temporally stable (sorry, no citation off hand), but there are hacks - e.g. self-control strategies like mental contrasting, implementation intentions, learned industriousness, etc... can partially achieve the same effect as having more conscientiousness.

This is a good question though... I will investigate some more.

This is my own thought and not backed up by any citations, but ...

Since Concientiousness is usually measured by self-reporting, you could find a Concientiousness survey and turn all the questions into affirmations, and recite these affirmations daily. "How often do you forget important deadlines?" -> "I rarely forget important deadlines." I would hypothesize that eventually you might come to believe these discrete facts about yourself. Directly, this would lead to much higher scores on future Concientiousness surveys.

I've read that the only "cure" for true personality disorders is to fake it until faking it becomes second nature. For example, narcissists pretend to care about the needs of others until they sort of start to automatically care about them. So my idea here is that by pretending to have higher Concientiousness, you might actually change.

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.

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.

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 "super sensitivities" that predict moral behavior. There may be a way to increase these - perhaps with drugs or life experiences designed to make your nervous system more excitable.

See also Jane Elliot's brown eyes, blue eyes experiment. I don't know whether they did these formally, but they observed that when the situation was reversed (the situation was that kids with a certain eye color were told they were better and became abusive) the children who had experience being second class were much less abusive when put into the "better than" role, as if the experience of being second class had inoculated them against some amount of the bad behavior.

I researched violent crime one day and discovered that the main thing that was connected with violent crime was high testosterone. In theory, treatment using existing drugs could make a very big difference. That would probably require some kind of training intended to explain to the violent criminals that their problem was chemical, and convince them to take the drugs. This would be difficult because if they're chemically imbalanced it may not be easy to get that through to them. To an ordinary person, it's a no-brainer, but to them, it's probably not. Some type of educational program designed to get them to wake up and realize they need testosterone reduction treatment may go a long way.

This doesn't exactly qualify as training, as I've gone up to a meta level, but this kind of thinking could potentially make a very big difference:

We need to consider the role of perverse incentives. There are a lot of perverse incentives in life, and a lot of them are improperly checked and balanced. For instance, diagnosing a person with a mental disorder can be devastating to that person and to come up with an accurate diagnosis can take some time. However, psychologists are pressured to diagnose on the first visit because they can't get paid by the insurance company without it. Take a good person and put them into a bad situation, and they may react as if they were a bad person because they need to in order to survive. Identifying and changing perverse incentives might really change not only the way that a large number of people behave, but would also redirect the selection pressure on humans such that the good ones are more likely to survive and reproduce, helping to "train" our genes in the right direction, rather than just our behavior.