Instead of using 'Promoted to front page' publishing option, just use 'Published' and Views 2. Set up a view of a page, for example with URL 'current', which you set as the default front page at Site Information > Default front page. Then set up Views to filter newsletters for published newsletters, sorted by Posted date: descending, no pager, and Items to display: 1. This will show on the 'current' frontpage only the most recently published newsletter (as long as posted dates are in chronological order).
Just publish your newsletters as scheduled and they will automatically be rotated off the frontpage. Leave the old ones published to view in archives.