What you need to do is to create another site group, besides the
Contributor and Reader.

Where do I create new site groups? In the Manage Users screen?

its available in the site setting and if its an are in the SPS then its
available in the action pane called manage security

Follow these steps:

1. At the portal level, click on Site Settings.
2. Under the General Settings section, click on the Manage security and
additional settings link.
3. Under the Users and Permissions section, click on the Manage site groups
link.
4. Click add  a Site Group.
5. Give it a name and assign the rights for this site group. If you don't want
the user to delete, then don't check the delete  Items checkbox.