Angular 2 has a custom login: https://auth0.com/docs/quickstart/spa/angular2/02-custom-login
But I can't find any for AngularJS, https://auth0.com/docs/quickstart/spa/angularjs
Is it not possible to have a custom login with AngularJS? Or do I need to manually use an API on the back-end?
It's possible to achieve the same functionality either by using Angular 1.X or Angular2. In this case, it's just a mismatch in the available sample code.
You would do this using the same Auth0 library, Auth0.js, that is being used in the Angular2 sample to achieve the custom login, so you can use that code as a baseline of what you need to do and adapt it from Angular2 to Angular 1.X or you can also check the documentation of the Auth0.js library itself; the section about single page apps would likely be the most useful.