Center Aligning Labels in a enumerate environment

I would use a description list here instead of misusing itemize. In order for this to work you need to specify the longest label you will have. You need to have enumitem calculate the left margin for you, using leftmargin=!.

\documentclass{article}
\usepackage{enumitem}
\usepackage{calc}
\newlength{\mylongest}
\setlength{\mylongest}{\widthof{The longest label I will need}}
\addtolength{\mylongest}{\labelsep}
\SetLabelAlign{CenterWithParen}{\makebox[\mylongest]{(#1)}}
\begin{document}
\begin{description}[style=unboxed,align=CenterWithParen,labelwidth=\mylongest,leftmargin=!]
\item[Foo]{This is a foo item}
\item[FooBar]{This is a foobar item}
\item[A longer description]{A longer label}
\end{description}
\end{document}

One can use environ and so avoid guessing at the widest label.

\documentclass{article}
\usepackage{enumitem}
\usepackage{environ}
\newlength{\cdescwidth}
\SetLabelAlign{CenterWithParen}{\makebox[\cdescwidth]{\normalfont(#1)}}

\NewEnviron{cdesc}{%
  \setbox0=\vbox{% measure the label widths
    \global\cdescwidth=0pt
    \def\item[##1]{%
      \settowidth{\dimen0}{(##1)}%
      \ifdim\dimen0>\cdescwidth
        \global\cdescwidth=\dimen0
      \fi}
    \BODY}
  % set the label width
  \global\advance\cdescwidth\labelsep
  \begin{description}[
    font=\normalfont,
    style=unboxed,
    align=CenterWithParen,
    labelwidth=\cdescwidth,
    leftmargin=!
  ]
  % typeset the contents
  \BODY
  \end{description}
}

\begin{document}
\begin{cdesc}
\item[Foo] This is a foo item
\item[FooBar] This is a foobar item
\item[A longer description] A longer label
\end{cdesc}
\end{document}

A different implementation with expl3 that avoids the tentative typesetting of the whole lot.

\documentclass{article}
\usepackage{enumitem}
\usepackage{xparse}

\ExplSyntaxOn

\SetLabelAlign{CenterWithParen}{\makebox[\l__kan_cdesc_dim]{\normalfont(#1)}}

\NewDocumentEnvironment{cdesc}{+b}
 {
  \__kan_cdesc_setup:n { #1 }
  \begin{description}[
    font=\normalfont,
    style=unboxed,
    align=CenterWithParen,
    labelwidth=\l__kan_cdesc_dim,
    leftmargin=!
  ]
  % typeset the contents
  #1
  \end{description}
 }{}

\dim_new:N \l__kan_cdesc_dim

\cs_new_protected:Nn \__kan_cdesc_setup:n
 {
  \seq_set_split:Nnn \l__kan_cdesc_seq { \item } { [] #1 }
  \dim_zero:N \l__kan_cdesc_dim
  \seq_map_function:NN \l__kan_cdesc_seq \__kan_cdesc_measure:n
  \dim_add:Nn \l__kan_cdesc_dim { \labelsep }
 }
\cs_new_protected:Nn \__kan_cdesc_measure:n
 {
  \__kan_cdesc_measure_aux:w #1 \q_stop
 }
\cs_new_protected:Npn \__kan_cdesc_measure_aux:w [#1] #2 \q_stop
 {
  \hbox_set:Nn \l_tmpa_box {\normalfont(#1)}
  \dim_set:Nn \l__kan_cdesc_dim
   {
    \dim_max:nn { \box_wd:N \l_tmpa_box } { \l__kan_cdesc_dim }
   }
 }

\ExplSyntaxOff


\begin{document}
\begin{cdesc}
\item[Foo] This is a foo item
\item[FooBar] This is a foobar item
\item[A longer description] A longer label
\end{cdesc}
\end{document}