The dirty hack
This doesn't involve changing any .bst files, but will most certainly mess with the rest of your bibliography. If we look at the .bbl file created by bibtex we find
\newblock {\em The Journal of Narrative Technique}, ...
Hence we could redefine \em to expand to // em.
% arara: pdflatex
% arara: bibtex
% arara: pdflatex
% arara: pdflatex
\documentclass{article}
\begin{document}
\cite{doody}
{\em Emphasized text}
\let\oldem=\em % save \em
\def\em{//\space\oldem}
\bibliographystyle{plain}
\bibliography{biblatex-examples.bib}
\let\em=\oldem % restore \em
{\em Emphasized text}
\end{document}

Using biblatex
With biblatex everything is easier. We use
\renewbibmacro{in:}{...}
to suppress "In:" before the journal title and
\DeclareFieldFormat[article]{journaltitle}{// \emph{#1}}
to get the two slashes.
% arara: pdflatex
% arara: biber
% arara: pdflatex
% arara: pdflatex
\documentclass{article}
\usepackage{biblatex}
\renewbibmacro{in:}{\ifentrytype{article}{}{\printtext{\bibstring{in}\intitlepunct}}}
\DeclareFieldFormat[article]{journaltitle}{// \emph{#1}}
\addbibresource{biblatex-examples.bib}
\begin{document}
\cite{doody}
\printbibliography
\end{document}
(biblatex displays more fields than bibtex by default.)

titleandjournalfields -- and nowhere else? – Mico Jun 01 '14 at 11:17\begin{rant}Wouldn't it be easier adopting a standard?\end{rant}You have all my sympathy.;-)– egreg Jun 01 '14 at 12:13