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.