I read some more of J.S. Beck's Cognitive Therapy: Basics and Beyond

In order to change your core beliefs, she suggests any of the following methods

1. Socratic argumentation - dispute the irrational belief as if you were on a debate team
2. Behavior experimentation - test the irrational belief in the real world, and see if it holds up
3. Cognitive Spectrum - ex. it hurts me when others tease me, but if I tell myself, "at least I can trust them" then it makes the teasing less hurtful
4. Role-play rational/emotional selves - play a back n' forth scenario between your mind (which is trying to change your belief) and your heart (which is trying to hold onto the older belief)
5. Using others as a reference point - look at others with your new belief, and derive inspiration from them
6. As if - pretend as if your core belief was changed, what would you then do?
7. Self-explanation - vent yourself, and then try to reframe or redesign your belief-changing approach to suit it
8. Metaphors/Fables - use simple lessons or aphorisms (like Aesop's Fables) to dispute your irrational core belief

Unhelpful core beliefs also generally fall into two categories:

A. unlovability - ex. "I'm never good enough", "people hate me", and "I'm different"
B. helplesness - ex. "You can't be happy" and "nothing has meaning"