If you look at the code which defines your custom post type, you will probably find something like
'capability_type' => 'page',
Following the example in Justin’s article I linked to you can replace this with a custom capability type that you can define
So for a CPT called ‘snippets’ we could replace 'capability_type' => 'page',
with something like the following:
'capability_type' => 'snippet',
'capabilities' => array(
'publish_posts' => 'publish_snippets',
'edit_posts' => 'edit_snippets',
'edit_others_posts' => 'edit_others_snippets',
'delete_posts' => 'delete_snippets',
'delete_others_posts' => 'delete_others_snippets',
'read_private_posts' => 'read_private_snippets',
'edit_post' => 'edit_snippet',
'delete_post' => 'delete_snippet',
'read_post' => 'read_snippet',
),
I am not familiar with the plugin called ‘access manager’ and could not find one with that name in the plugin directory (although there are a few similarly named ones)
In Justin’s Members plugin there is an easy way to add capabilities to a role, which in the case of my example allows me to add any or all of these capabilities to a role without needing to grant the equivalent capabilities for managing posts/pages.
if you cannot find an option to do this in your plugin, you will need to ask the plugin author whether it is possible.