I'm slightly confused (easy for me). If you (as admin) create the category, and in this category you add the necessary albums, you should be able to set the permissions for that category.
This can be set by category and user group, so for example, you can allow your users to create albums in category "A" but disallow them to create albums in category "B, but still allow them to upload images.
Below is a quote from the category properties settings,
"In coppermine versions before cpg1.5.x, only the admin was allowed to create albums within public (i.e. admin-created) categories. Starting with cpg1.5.x, this has changed: by default, non-admin users can't create albums, but the administrator can decide to allow them to create albums. This can be set by category and user group, so you can allow your users to create albums in category "A" but disallow them to create albums in category "B". This is why there is an additional list box in the category control panel named "Group(s) allowed to create albums in this category" where you (as admin) can specify the groups you wish to allow. The admin group is not being listed there, as the admin can create albums anyway and doesn't need specific permissions.
Choose one or more groups from the list to allow those groups to create albums within the category you're editing. To select multiple groups, hold the [Ctrl]-key down and click on the groups. To de-select all groups, use the [Ctrl]-button as well and click on the last selected group."