"Are there any alternatives?" There's biblatex (which features a natbib compatibility option). The additional package options style=authoryear,maxcitenames=2 should result in an output that is fairly close to natbib. To add ", Paper~x" after the year of some bibentries,
add the paper number as the usera field in the .bib file for those entries;
define a bibmacro that will print ", Paper~" plus the content of the usera field if this field is defined;
add the above bibmaco to the format definition of labelyear (if extrayear is empty) and extrayear;
in case you don't want ", Paper~x" in the bibliography, add \AtEveryBibitem{\clearfield{usera}}.
\documentclass{article}
\usepackage[style=authoryear,maxcitenames=2,natbib=true]{biblatex}
\newbibmacro*{papernum}{%
\iffieldundef{usera}{%
}{%
\addcomma\space
Paper~\printfield{usera}%
}%
}
\DeclareFieldFormat{labelyear}{%
\stripzeros{#1}%
\iffieldundef{extrayear}{%
\usebibmacro{papernum}%
}{%
}%
}
\DeclareFieldFormat{extrayear}{%
\iffieldnums{labelyear}
{\mknumalph{#1}\usebibmacro{papernum}}
{\mkbibparens{\mknumalph{#1}\usebibmacro{papernum}}}}
\AtEveryBibitem{\clearfield{usera}}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@misc{A01,
author = {Author, A.},
year = {2001},
title = {Alpha},
}
@misc{Mil12x,
usera = {1},
author = {Miller, M. and Author, A. and Buthor, B.},
year = {2012},
title = {Malcom},
}
@misc{Mil12y,
usera = {2},
author = {Miller, M. and Author, A. and Buthor, B.},
year = {2012},
title = {Mike},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\citet{Mil12x}
\citep{Mil12x}
\citet{A01,Mil12y}
\citep{A01,Mil12y}
\printbibliography
\end{document}

\citetaliasand\citepalias"function much like\citetand\citep: they may take multiple keys in the argument, may contain notes, ...". Assuming that the key to the Miller piece is "miller" and you've already set\defcitealias{miller}{Miller et al.}, you might give\citetalias[2012, Paper 1]{miller}and\citepalias[2012, Paper 1]{miller}a try. – Mico May 5 '12 at 13:42\citet[Paper 1]{miller}and\citep[Paper 1]{miller}. – Mico May 5 '12 at 14:27