How to resolve the MySQL error Duplicate entry 'comment_publish_action' for key 'PRIMARY'?
From the information provided in the question so far, it is hard to tell what is causing your problem (consider refining your question by editing it).

However, as an alternative, you may want to consider using the Backup and Migrate module like so:


install that module on both Drupal sites (where you want to export from, and where you want to import to).
use this module to create a backup in the originating Drupal site (and save it somewhere to a local file), of the relevant tables in the MySQL database.
use this module to restore that "local file" (= backup) to import it in your target site (which is where you're currently encountering the problem.


Does this help somehow?