How to enable comments on custom entities
For Drupal 7, this module should do it - https://www.drupal.org/project/comments_entity

For Drupal 8, comments are available as a field for any entity type.

Summary:


Create a new Entity Type
Create a new Bundle for that Entity Type
Create a new Comment Type and select your Entity Type
"Manage Fields" on your new Bundle and add a new "Comments" field.
Configure comments as desired in the field settings.


Wrote a blog post about it here: http://www.daggerhart.com/drupal-8-add-comments-custom-entity-type/