The best replacement for hyperbole is metaphor.

The best alternatives to hyperbole are rated as following:
★★★★★  metaphor
★★★★  exaggeration
★★★★  idiom
★★★  simile
★★  understatement
★★  personification
★  sarcasm
★  idioms
  overstatement
  figurative language
  analogy
  metaphors

Your alternative for hyperbole is not listed? Suggest!
Speaking about hyperbole, one probably shouldn't forget about picture books.

Other search terms related to hyperbole and their ratings are:
★★★★★ picture books
★★★ poems
You have in mind a companion for hyperbole and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of hyperbole in all years. Click on graph for more.
hyperbole
metaphor
exaggeration