Well, if you are ONLY looking for a specific help about the ID of those vehicles, maybe this post would be better in "Cars and Movies" or in "General" section.

If it is here, I understand you want in the site these pictures and, perhaps, there they will be identified.

About the buggy I don't know nothing about it and and about the Chevy the only thing I can add is that it's a 1939 but, as you said before, I don't know if it's a Funeral Coach or Van. Certainly looks like its body comes from an idependent car body maker.

The Buggy: not a character itself, but shown very often since it is used by the kids and cousin to explore Auckland. Due to this frequency, I'd give it 3 stars.

The Black Chevy: this one is more distinctive as a "mothership" for the slimy monsters, and it is shown very often too, but it is not the absolute star at all (not Herbie, I mean), so I'd give it a 3-4 stars.

Both of the cars are shown in most 8 episodes, but more frequently from 1st thru 4th.

Hope this helps.

Star of each vehicle?

Season and Episode?
http://akas.imdb.com/title/tt0202769/episodes

Here you are a couple of cars featured in NZTV cult series "Under The Mountain". I know nothing about the buggy, and the black car looks like a 1939 Chevrolet Master Deluxe, but longer, like an ambulance or even a hearse version. Any suggestions?