I know this was posted awhile ago, but if you're still here, I'm happy to help! I live in Piura, and your best bet is to look at the universities, Universidad de Cesar Vallejo or Universidad de Piura. I am not sure about UAP or the National university. I also heard rumor of the Montessori school needed an English teacher for children, but I am not sure about that.
Please let me know if I can help you out more. I work at one university, and I have friends at the other.