The best replacement for fairy tale is fable.

The best alternatives to fairy tale are rated as following:
★★★★★  fable
★★★★  folk tale
★★★  fantasy
★★★  folktale
★★★  myth
★★  fairytale
★★  tall tale
  fairy tail
  tale
  nursery rhyme
  legend
  fairy tale

Your alternative for fairy tale is not listed? Suggest!
Speaking about fairy tale, one probably shouldn't forget about socks under the bed.

Other search terms related to fairy tale and their ratings are:
★★★★★ socks under the bed
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fairy tale
fable
folk tale