To send a password reset email you can use the API endpoint /publisher/user/resetPassword.
The AID and e-mail address are specified as parameters and once called, the user will receive a password reset email.
Sample request for an application on the US dashboard:
https://api.piano.io/api/v3/publisher/user/resetPassword?api_token=xxx&aid=xxx&email=test@test.com
A list of base URLs for other dashboards can be found here.
Please note, that this ID Password reset request email notification under Email Manager needs to be enabled.