From episode 1.20, it's a 1950 Dodge Woody Station Wagon:
http://evenstevens.disneytvzone.com/media/evenstevens/gallery/pictures/season1/2- 0-almost_perfect/img149.jpg


And now, from the opening theme, thanks to the only episode available on DVD in the United States, The Stevens family's 1995-99 Ford Explorer!!!:




This show in general really ought to be on DVD. I've read somewhere that it already is in Austrailia.