While "parabula" is the most direct translation, there are other words you could use depending on the context:
* Kuwentong pambata (Children's story)
* Kwento ng hayop (Animal story)
* Alamat (Legend)
It's important to note that "alamat" is closer to a myth or folktale, but can also be used to refer to fables in some cases.
Ultimately, the best way to choose the right Tagalog word is to consider the specific fable you're talking about and the context of your communication.