Fake italic small-caps are not recommended, any more than fake small-caps or fake italic. In general, faked glyphs always involve a compromise in quality.
This answer highlights a few options for real italic and oblique small-caps, including an option for a Times-like font.
[I am not sure that 'oblique' and 'italic' are distinct in the case of small-caps, so am just covering all possible eventualities.]
Latin Modern provides italic small-caps fonts but these are not supported by the default lmodern support package. cfr-lm does support them, however:
\documentclass{article}
\usepackage{cfr-lm}
\begin{document}
The following three are equivalent:
\begin{enumerate}
\item \textsi{Small-caps Italic}
\item \textit{\textsc{Italic Small-caps}}
\item \textsc{\textit{Small-caps Italic}}
\end{enumerate}
\end{document}

The same code works for
\usepackage{venturis}

\usepackage{electrum}

\usepackage{berenis}

TeX-Gyre Termes is an enhanced clone of Times which includes italic small-caps:

\documentclass{article}
\usepackage{tgtermes}
\begin{document}
\fontshape{scit}\selectfont Italic Small-caps
\end{document}
\textscnottextsf– Seamus Oct 28 '11 at 07:27\usepackage{smallcap}. – jeecabz Jan 28 '14 at 10:00