I need to create a unique permission group that would have all the same rights as a Contributor accept remove the ability to Delete. Is this possible without writing code?

Yes, you can do this code-free (I too have had the need for the same permission set). Go to the top level of your SharePoint Site > Site Actions > Site Settings > Advanced Permissions > Settings > Permission Levels > Click on "Contribute" (not the check box) > Click "Copy Permission Level" (at the bottom of the page) > Enter an identifying name for the new permission level (i.e. Contribute Without Delete) > Uncheck the box next to "delete items" > Click "Create You may now assign this to users/groups.