Such a rotation is not a big deal -- Ditto snippet provides us with almost all means that are necessary for solving this task.
[!Ditto? &parents=`x,y,z,...` &display=`1` &start=`offset` &tpl=`product-template` ...and-possibly-some-other-params... !]
I listed crucial parameters for products rotation. "x,y,z" is a folders list where products are stored; &display specifies that we are grabbing exactly one product; &tpl specifies how it should be rendered; and &start actually does the rotation. Of course, we need to arrange start’s changing on a daily basis. Luckily, PHP function date is a perfect opportunity for such arrangement. We can create one-line snippet:
return date('z', time());
This snippet returns current yearday (0..365). Now you only need to connect this snippet instead of the offset. Done. On Jan 1st application will display first product, on Jan 2nd -- second, etc. If you are not satisfied with this simple rotation, you can develop this suggestion and create something more sophisticated. Enjoy!