Generally to grant access to the custom post type, like ‘Podcasts’:
Go to the “Users->User Role Editor” page and look at the “Custom post types->Podcasts” group. If it contains unique user capabilities, like edit_podcasts, then grant needed of them to the contributor role, similar to the ‘Posts’.
If it contains the same ‘edit_posts’, etc., read this article:

Manage access to the custom post types?

In order to convert editor role back to the contributor you have to revoke from it edit_published_% (like ‘edit_published_posts’) and publish_% (like publish_posts) capabilities.