In-text citation
In-text citation: (Campbell u. Pedersen 2007)
In-text citation with more than two authors: (Campbell et al. 2007)
In-text citation with single page: (Campbell u. Pedersen 2007, S. 25)
In-text citation with several pages: (Campbell u. Pedersen 2007, S. 25-26)
In-text citation with several releases in the same year and mixed number of pages: (Campbell u. Pedersen 2007a, S. 25-28, 2007b, S. 81, 91)

New rule since 2017:
No abbreviations like "ebd." (same author), "f." (citation is on given page and adjacent page), "ff." (citation is on given page and a span of adjacent pages) or "vgl." (indirect citation) or "op. cit.".
Footnotes on same page, no endnotes.

Bibliography

Journal article:
Campbell, John L., und Ove K. Pedersen. 2007. The varieties of capitalism and hybrid success. Subheading for article also included. Comparative Political Studies 40(3): 307–332. DOI: 10.1177/0010414006286542.
( I interpret 40(3) as volume(issue) )

Book chapter:
Mares, Isabella. 2001. Firms and the welfare state: When, why, and how does social policy matter to employers?. In Varieties of capitalism. The institutional foundations of comparative advantage, Hrsg. Peter A. Hall und David Soskice, 184–213. New York: Oxford University Press.

Additional info on bibliography:
Book:
Hall, Peter A., und David Soskice (Hrsg.). 2001. Varieties of capitalism. The institutional foundations of comparative advantage. New York: Oxford University Press.

Book with 4 editors, primary publication date and two places:
Hall, Peter A., David Soskice, John Doe, und Jane Doe (Hrsg.). [1984] 2001. Varieties of capitalism. The institutional foundations of comparative advantage. New York/Amsterdam: Oxford University Press.
(All Editors and all Authors are always fully mentioned in bibliography, no abbreviations like "et al.")

Examples and guidelines:
Here's the most recent openly accessible article from this journal that uses new guidelines (PVS seems to be completely closed otherwise, no open access at all):
https://www.nomos-elibrary.de/10.5771/0032-3470-2016-4-560/state-de-construction-in-iraq-and-syria-jahrgang-57-2016-heft-4?page=1
Note that this english article uses "and" instead of the German "und".

Here are the most recent guidelines for authors who submit articles to the journal:
http://www.pvs.nomos.de/fileadmin/pvs/doc/PVS_Autorenhinweise_2017_deutsch.pdf

What's wrong with existing style
- Delimiters: must be "u." in in-text citation and "und" in bibliography
- Almost always dots, commas only between Surname-Prename and no colons: In bibliographies it's always: Surname, Prename. 2010. etc. (see below)
- Editors and book title in wrong order.
- Page numbers after editors, not at the end.

See this comparison - First one according to most recent guidelines, second one is made with the style available on Zotero.

Mares, Isabella. 2001. Firms and the welfare state: When, why, and how does social policy matter to employers?. In Varieties of capitalism. The institutional foundations of comparative advantage, Hrsg. Peter A. Hall und David Soskice, 184–213. New York: Oxford University Press.

Mares, Isabela, 2001: Firms and the Welfare State: When, Why, and How Does Social Policy Matter to Employers?, in: Hall, Peter A./Soskice, David (Hrsg.), Varieties of Capitalism. The Institutional Foundations of Comparative Advantage. New York: Oxford University Press, 184–213.

Also note that the English article I provided you with uses "eds." for mentioning the editors instead of "Hrsg.", as it should be in the German version of this style.

And, as seen in the example, I suppose it is not necessary to add a dot after the title in the bibliography when the title already comes with a punctuation mark like "?" or "!". So it should be:
When, why, and how does social policy matter to employers?[.] In Varieties of capitalism.

Thanks for the quick replies!

Almost there!

First of all, thanks a lot for your good work! Improving this style will probably be a great service to German students of political science, since this is one of the main citation styles in this discipline. This will be really helpful!

Some bugfixing needs to be done:
There is one space charakter missing before the year specification: (following example is created with the update style and problems are highlighted in bold)
Muhle, Maria.[ ]2011. Jacques Rancière. Für eine Politik des Erscheinens[.] In Kultur. Theorien der Gegenwart.[,] Hrsg. Stephan Moebius, und Dirk Quadflieg, 311–320. Wiesbaden: VS Verlag.

Bibliography entries for book chapters:
As you can see in this example there is no automatically placed dot after the title of the book chapter. This is ok, considering the possibility that the title itself could already come with a punctuation mark, like "?" or "!" and in these cases, there is no need for a dot. If we keep it this way, it's up to the Zotero users to add the dot in the field manually and for the aforementioned cases, this increases flexibility.

But: This collides with the now included automatic dot placement after the book title.
First, there needs to be a comma after the book's title.
Second, this is the same issue as with the chapter's title and its included punctuation marks. This should be the same rule for both cases: Either leave the dot and comma completely up to the user or add somekind of a punctuation mark detection algorithm. (Don't know if that's possible)

Ok, good to know.
Well, then there should definitely be a period after the chapter title and a comma after the book title.

Sorry about the confusion I caused with the punctuation.

thanks for the quick replies!
The automatic period suppression is not working. I get "?." or "?," after chapter and book title.

Alright, we're on a good way. This solved the problem for the chapter title. Still, the same issue persists with the book title: "?,".
See the example below.

Rancière, Jacques. 2011. Wer ist das Subjekt der Menschenrechte? In Die Revolution der Menschenrechte. Grundlegende Texte zu einem neuen Begriff des Politischen?, Hrsg. Christoph Menke, Frankfurt a.M.

Alright, I'm fine with that. Since the book title is italicized, for me, this is no problem, aesthetically. To be honest, I'm not 100% sure about the rule for suppressing the commas. The journal's guidelines don't go into detail on this matter and I don't have access to another article, so I can't look up further examples for this case.

Thank's a lot for your work! I've been waiting for this for quite a few years now and I'm very happy that this request was processed so fast. Excellent work!

Thanks. I submitted the Pull Request.
edit: Adam accepted it and the new style will be updated shortly on the repository. Check the time stamp.
https://www.zotero.org/styles?q=id:politische-vierteljahresschrift