The appropriate possessive suffix can be generated by examining the last few characters of the label. This is straightforward using the package xstring.
Possessive citation commands in English are much easier to construct. An example under the the standard author-year styles is covered in another question.
authoryear and its variants
In response to a feature request on possessive citations, Philipp Lehman demonstrated how one could generate a possessive labelname in English using a format alias. The code below extends this approach to other types of labels and Norwegian possessives. It should work for all variants of the standard author-year styles.
\documentclass{article}
\usepackage[norsk]{babel}
\usepackage[style=authoryear-comp]{biblatex}
\usepackage{xstring}
\usepackage{filecontents}
\newrobustcmd*{\mkbibpossess}[1]{%
\IfEndWith{#1}{s}
{'}
{\IfEndWith{#1}{sh}
{'}
{\IfEndWith{#1}{sj}
{'}
{\IfEndWith{#1}{z}
{'}
{s}}}}}
\DeclareNameFormat{labelname:poss}{% Based on labelname from biblatex.def
\ifcase\value{uniquename}%
\usebibmacro{name:last}{#1}{#3}{#5}{#7}%
\or
\ifuseprefix
{\usebibmacro{name:first-last}{#1}{#4}{#5}{#8}}
{\usebibmacro{name:first-last}{#1}{#4}{#6}{#8}}%
\or
\usebibmacro{name:first-last}{#1}{#3}{#5}{#7}%
\fi
\usebibmacro{name:andothers}%
\ifthenelse{\value{listcount}=\value{liststop}}
{\ifmorenames
{s}
{\StrRemoveBraces{#1}[\cbxnobraces]%
\IfEndWith{\cbxnobraces}{s}
{'}
{\IfEndWith{\cbxnobraces}{sh}
{'}
{\IfEndWith{\cbxnobraces}{sj}
{'}
{\IfEndWith{\cbxnobraces}{z}
{'}
{s}}}}}}
{}}
\DeclareFieldFormat{shorthand:poss}{%
\ifnameundef{labelname}{#1\mkbibpossess{#1}}{#1}}
\DeclareFieldFormat{citetitle:poss}{\mkbibemph{#1}\mkbibpossess{#1}}
\DeclareFieldFormat{label:poss}{#1\mkbibpossess{#1}}
\newrobustcmd*{\posscitealias}{%
\AtNextCite{%
\DeclareNameAlias{labelname}{labelname:poss}%
\DeclareFieldAlias{shorthand}{shorthand:poss}%
\DeclareFieldAlias{citetitle}{citetitle:poss}%
\DeclareFieldAlias{label}{label:poss}}}
\newrobustcmd*{\posscite}{%
\posscitealias%
\textcite}
\newrobustcmd*{\Posscite}{\bibsentence\posscite}
\newrobustcmd*{\posscites}{%
\posscitealias%
\textcites}
\begin{filecontents}{\jobname.bib}
@Book{kish,
author = {Kish, Leslie},
title = {Survey Sampling},
publisher = {John Wiley and Sons},
address = {New York},
year = {1965}}
@Online{hss,
author = {{U.S. Dept. of Health and Human Services}},
url = {http://www.hhs.gov},
year = {2011}}
@Report{nasa,
title = {Fiscal Year 2012 Budget Estimates},
author = {{National Aeronautics and Space Administration}},
shortauthor = {NASA},
year = {2011}}
@Book{shorthand,
shorthand = {Shorthand sj},
year = {2010},
publisher = {Anonymous Press},
location = {New York}}
@Book{label,
label = {Label z},
year = {2011},
publisher = {Anonymous Press},
location = {New York}}
@Book{noauthors,
title = {A Book without Authors},
year = {2011},
publisher = {Anonymous Press},
location = {New York}}
@Book{noauthor,
title = {A Book with No Author},
year = {2011},
publisher = {Anonymous Press},
location = {New York}}
@Manual{dyna:browser,
title = {Dynatext, Electronic Book Indexer/Browser},
organization = {Electronic Book Technology Inc.},
address = {Providence, RI},
year = {1991}}
\end{filecontents}
\addbibresource{\jobname.bib}
\bibliography{biblatex-examples}
\renewcommand{\baselinestretch}{1.25}
\begin{document}
\subsection*{label ending in s/sh/sj/z}
Author ending in sh: \posscite[45--68]{kish} \\
Author ending in s: \posscite[45--68]{gillies} \\
Corporate author ending in s: \posscite{hss}
No author, title ending in s: \posscite[45--68]{noauthors} \\
No author or title; shorthand ending in sj: \posscite[45--68]{shorthand} \\
Author ending in z: \posscite[45--68]{gonzalez} \\
No author, title or shorthand; label ending in z: \posscites{label}{gillies}
\subsection*{label ending in other characters}
Manual by organization: \posscite{dyna:browser} \\
Shortauthor: \posscite[45--68]{nasa} \\
Shorthand: \posscite[45--68]{kant:ku} \\
No author: \posscite[45--68]{noauthor} \\
Compact labelname: \posscites{aristotle:physics}{aristotle:poetics}
\end{document}

chicago-authordate
The approach for this style is similar, but when the label is generated by the bibliography macro cite:label it can take on many different formats depending on the entry type and available fields. So the code below redefines the macro locally for use by the possessive citation command.
\documentclass{article}
\usepackage[norsk]{babel}
\usepackage[authordate]{biblatex-chicago}
\usepackage{xstring}
\usepackage{filecontents}
\newrobustcmd*{\mkbibpossess}[1]{%
\IfEndWith{#1}{s}
{'}
{\IfEndWith{#1}{sh}
{'}
{\IfEndWith{#1}{sj}
{'}
{\IfEndWith{#1}{z}
{'}
{s}}}}}
\DeclareNameFormat{labelname:poss}{% Based on labelname from biblatex.def
\ifcase\value{uniquename}%
\usebibmacro{name:last}{#1}{#3}{#5}{#7}%
\or
\ifuseprefix
{\usebibmacro{name:first-last}{#1}{#4}{#5}{#8}}
{\usebibmacro{name:first-last}{#1}{#4}{#6}{#8}}%
\or
\usebibmacro{name:first-last}{#1}{#3}{#5}{#7}%
\fi
\usebibmacro{name:andothers}%
\ifthenelse{\value{listcount}=\value{liststop}}
{\ifmorenames
{s}
{\StrRemoveBraces{#1}[\cbxnobraces]%
\IfEndWith{\cbxnobraces}{s}
{'}
{\IfEndWith{\cbxnobraces}{sh}
{'}
{\IfEndWith{\cbxnobraces}{sj}
{'}
{\IfEndWith{\cbxnobraces}{z}
{'}
{s}}}}}}
{}}
\DeclareListFormat{organization:poss}{%
\usebibmacro{list:delim}{#1}%
#1\isdot
\usebibmacro{list:andothers}%
\ifthenelse{\value{listcount}=\value{liststop}}
{\ifmoreitems
{s}
{\StrRemoveBraces{#1}[\cbxnobraces]%
\IfEndWith{\cbxnobraces}{s}
{'}
{\IfEndWith{\cbxnobraces}{sh}
{'}
{\IfEndWith{\cbxnobraces}{sj}
{'}
{\IfEndWith{\cbxnobraces}{z}
{'}
{s}}}}}}
{}}
\DeclareFieldFormat{shorthand:poss}{%
#1\mkbibpossess{#1}}
\DeclareFieldFormat{possess}{\mkbibpossess{#1}}
\newbibmacro*{cite:label:poss}{% Based on cite:label from chicago-authordate.cbx
\iffieldundef{label}%
{\iffieldequalstr{entrysubtype}{magazine}%
{\printtext[bibhyperref]{%
\printfield[journaltitle]{journaltitle}%
\printfield[possess]{journaltitle}}}%
{\iffieldequalstr{entrytype}{manual}%
{\printtext[bibhyperref]{\printlist{organization}}}%
{\printtext[bibhyperref]{%
\printfield[citetitle]{labeltitle}%
\printfield[possess]{labeltitle}}}}}%
{\printtext[bibhyperref]{%
\printfield{label}%
\printfield[possess]{label}}}}
\newrobustcmd*{\posscitealias}{%
\AtNextCite{%
\renewbibmacro*{cite:label}{\usebibmacro{cite:label:poss}}%
\DeclareNameAlias{labelname}{labelname:poss}%
\DeclareListAlias{organization}{organization:poss}%
\DeclareFieldAlias{shorthand}{shorthand:poss}}}
\newrobustcmd*{\posscite}{%
\posscitealias%
\textcite}
\newrobustcmd*{\Posscite}{\bibsentence\posscite}
\newrobustcmd*{\posscites}{%
\posscitealias%
\textcites}
\begin{filecontents}{\jobname.bib}
@Book{kish,
author = {Kish, Leslie},
title = {Survey Sampling},
publisher = {John Wiley and Sons},
address = {New York},
year = {1965}}
@Online{hss,
author = {{U.S. Dept. of Health and Human Services}},
url = {http://www.hhs.gov},
year = {2011}}
@Report{nasa,
title = {Fiscal Year 2012 Budget Estimates},
author = {{National Aeronautics and Space Administration}},
shortauthor = {NASA},
year = {2011}}
@Book{shorthand,
shorthand = {Shorthand sj},
year = {2010},
publisher = {Anonymous Press},
location = {New York}}
@Book{label,
label = {Label z},
year = {2011},
publisher = {Anonymous Press},
location = {New York}}
@Book{noauthors,
title = {A Book without Authors},
year = {2011},
publisher = {Anonymous Press},
location = {New York}}
@Book{noauthor,
title = {A Book with No Author},
year = {2011},
publisher = {Anonymous Press},
location = {New York}}
@Manual{dyna:browser,
title = {Dynatext, Electronic Book Indexer/Browser},
organization = {Electronic Book Technology Inc.},
address = {Providence, RI},
year = {1991}}
\end{filecontents}
\addbibresource{\jobname.bib}
\bibliography{biblatex-examples}
\renewcommand{\baselinestretch}{1.25}
\begin{document}
\subsection*{label ending in s/sh/sj/z}
Author ending in sh: \posscite[45--68]{kish} \\
Author ending in s: \posscite[45--68]{gillies} \\
Corporate author ending in s: \posscite{hss}
No author, title ending in s: \posscite[45--68]{noauthors} \\
No author or title; shorthand ending in sj: \posscite[45--68]{shorthand} \\
Author ending in z: \posscite[45--68]{gonzalez} \\
No author, title or shorthand; label ending in z: \posscites{label}{gillies}
\subsection*{label ending in other characters}
Manual by organization: \posscite{dyna:browser} \\
Shortauthor: \posscite[45--68]{nasa} \\
Shorthand: \posscite[45--68]{kant:ku} \\
No author: \posscite[45--68]{noauthor} \\
Compact labelname: \posscites{aristotle:physics}{aristotle:poetics}
\end{document}

biblatex-chicagoI get an extra comma (Samarin's (, 1994b)...), butbiblatex-authoryeartranslates the bibliography just as well as -chicago, and switching over actually solved some other minor problems as well. Thanks a lot! – Pernille Jul 04 '11 at 13:53