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Is there a word meaning "ability to overcome boredom", just like how courage means "ability to overcome fear"?

Sample sentence: "It takes a lot of _ to read that book. I couldn't read it because it was so boring".

Determination and will don't really work since they apply to just about every emotion. I'm looking for something specific to boredom.

Boredom has many aspects and as such can have more than one "opposite" concepts that would fit in your example sentence. Consider for example:

It takes a lot of concentration to read that book. I couldn't read it because it was so boring.

vs.:

It takes a lot of curiosity to read that book. I couldn't read it because it was so boring.

or:

It takes a lot of stamina to read that book. I couldn't read it because it was so boring.

"It takes a lot of perseverance to read that book. I couldn't read it because it was so boring."

[Merriam-Webster]

: continued effort to do or achieve something despite difficulties, failure, or opposition : the action or condition or an instance of persevering : STEADFASTNESS

// She will always be fondly remembered for her perseverance and determination with a 'never give up' attitude.
— Hartford Courant, courant.com, "Ann Kelly," 14 July 2018

Note that perseverance applies to overcoming more things than just boredom. But I am unaware of any word that specifically means perseverance in the face of boredom.

Courage might specifically mean perseverance in the face of fear, but courage can also apply to an action that lasts for mere seconds. When spending hours reading a boring book, it's the quality of sustained effort that's relevant. Even if reading a few pages is a chore, you can't really be said to have perseverance (or overcome your boredom) if you give up after those few pages.

Psychologists might talk about this in terms of (behavioral or academic) self-regulation (see Wikipedia), which is the ability to make ourselves do things we'd rather not (or stop ourselves doing things we'd rather). It's not limited to boredom, though; you also need self-regulation to overcome distaste or anxiety, as well as to avoid temptation.

Two highly relevant components of self-regulation are motivation and self-control or willpower. It might sound like the latter is the same thing as self-regulation, but all the willpower in the world isn't going to get you through that boring book if you don't have a good reason to read it (and conversely, very high motivation probably won't get you there if you lack all willpower).

Some examples of use:

“I characterize boredom as a deficiency in self-regulation,” Danckert [a cognitive neuro-scientist who studies boredom] says.

—Maggie Koerth-Baker, "Why Boredom Is Anything but Boring", Scientific American, January 18, 2016

Boredom in the Classroom: Addressing Student Motivation, Self-Regulation, and Engagement in Learning

—Gayle L. Macklem, SpringerBriefs in Psychology, 2015

Many important learning tasks feel uninteresting and tedious to learners. This research proposed that promoting a prosocial, self-transcendent purpose could improve academic self-regulation on such tasks.

—David S. Yeager et al., "Boring but Important: A Self-Transcendent Purpose for Learning Fosters
Academic Self-Regulation", Journal of Personality and Social Psychology, 2014, Vol. 107, No. 4, 559 –580 (quote is from the abstract; full PDF here)