In Lisbon try autojardim - http://www.autocarhire.net. All the other majors are there as well.
If you are not familiar with manual shift vehicles remember to specify automatic. However, bear in mind there will be an extra premium as there is not much demand for automatics this side of the pond.
You should probbaly look to rent somethng like a Renault Megane or similiar model or a station wagon/estate.
