Dominant themes in The Reluctant Journal include having your "mind studied" through psychological analysis: "I don't want anyone to study my mind. ... But Dad says I no longer have a choice."
Another theme is the violence--physical, emotional and psychological violence--of bullies. If we apply a metaphor of war and peace, then the violence of bullying is war while the absence of a bully's violence is peace.
Another critical theme is the emergence of a sound mind and psyche from the aftermath of violence spewn out by bullies. Again, peace is a metaphor for this emergence. Freedoms sought for and gained is yet another applicable metaphor.
Since war, peace and freedoms are useful applicable metaphors, songs sprung from the Vietnam War protest movement would do well as the foundation of a soundtrack for The Reluctant Journal.
For example, Chapter 1 opens with a reference to the psychologist whom Henry, our protagonist and first-person narrator, is taken by his dad to see. The psychologist's name is Cecil Levine and he is described as having long gray hair pulled back in a ponytail. This is a clear indication of Cecil's being of the Vietnam War era. Donovan's song "The Ballad of a Crystal Man" could make an appropriate theme song for psychologist Levine.
I read your faces like a poem, kalidescope of hate words
For seagull, I don't want your wings, I don't want your freedom in a lie
We also learn in Chapter 1 that Henry escapes into "Robot-Voice" to avoid talking about "IT" and to avoid feeling emotion in general: "The thing about speaking Robot is, it strips emotion out of everything." The Credence Clearwater Revival song "Fortunate Son" might very well fit as theme song for Henry, since the title and lyrics are in a painfully ironic discord.
It ain't me. It ain't me.
It ain't me. It ain't me, nooo.
I ain't no fortunate son.
It is also in this chapter that Henry comments about liking to write, which results in Cecil giving him a journal for "a private place to record [his] thoughts and feelings." Henry's first impulse is to through the journal in the trash, yet he later takes it back out. "Come in Out of the Rain" by Parliament might give a good background sound to Cecil's attempts to gently bring Henry to speak about "IT," the horrific actions of his older brother that took place seven months earlier.
Happiness and peace
Is getting more and more out of my reach [...]
You're gunning down your brothers [...]
But nobody's got sense enough to come in out of the rain [...]
When will the people stop fightin' each other?
Learning to give and help one another
We shall all be free
We shall all be free
We shall all be free some day
Oh, deep in my heart, I do believe
We shall all be free, some day
Other Vietnam War songs or other protest songs of the 1960s and 1970s might fill in the the other six slots for the soundtrack. YouTube, of course, is an excellent source for searching.