It is not possible to advertise a property for sale and for rent simultaneously on Zillow.
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, the sale listing would need to be removed from the site. Once the sale status has been removed, you may then list your rental through Zillow Rental Manager.