You can take the missing characters from a font that has them:
\documentclass{book}
\usepackage{fontspec}
\usepackage{minted}
\usepackage{newunicodechar}
\setmonofont{Ubuntu Mono}
\newfontfamily{\freeserif}{FreeSerif}
\newunicodechar{⦃}{\makebox[.5em]{\freeserif⦃}}
\newunicodechar{⦄}{\makebox[.5em]{\freeserif⦄}}
\begin{document}
\begin{minted}{java}
Π ⦃a : D₀⦄
\end{minted}
\end{document}

The red boxes are a pygmentize problem.
The characters are also in DejaVu Sans; here's how they appear (with also a workaround for the red boxes):
\documentclass{book}
\usepackage{fontspec}
\usepackage{minted}
\usepackage{newunicodechar}
\AtBeginEnvironment{minted}{%
\let\MINTEDPYGdefault\PYGdefault
\renewcommand\PYGdefault[2]{%
\ifstrequal{#1}{err}%
{\MINTEDPYGdefault{n}{#2}}%
{\MINTEDPYGdefault{#1}{#2}}%
}%
}
\setmonofont{Ubuntu Mono}
\newfontfamily{\freeserif}{DejaVu Sans}
\newunicodechar{⦃}{\makebox[.5em]{\freeserif⦃}}
\newunicodechar{⦄}{\makebox[.5em]{\freeserif⦄}}
\begin{document}
\begin{minted}{java}
Π ⦃a : D₀⦄
XXXXXXXXXX
\end{minted}
\end{document}

Missing character: There is no ⦃ in font Ubuntu Mono/OT:script=latn;language=DF LT;!– Johannes_B Mar 27 '15 at 15:49