It is not possible to advertise a property for sale and for rent, simultaneously on Zillow or Zillow Rental Manager. Zillow will only have one version of a listing active at any given time to prevent duplicates and spam, regardless of listing type or sources.
If you would like to advertise your property for rent, but you already have it listed for sale, you would need to deactivate the for sale listing first in order for your rental listing to show up.