Small letter e with double grave

The accent is available in standard pdflatex with tipa:

\documentclass{article}
\usepackage[safe]{tipa}

\begin{document}

\textdoublegrave{e}

\end{document}

You can also use direct input:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[safe]{tipa}

\DeclareUnicodeCharacter{0205}{\textdoublegrave{e}}

\begin{document}

\textdoublegrave{e} ȅ

\end{document}

With XeLaTeX or LuaLaTeX this is very easy:

% Use either xelatex or lualatex to compile this example
\documentclass{article}

\usepackage{fontspec}

\begin{document}
ȅ
\end{document}