Remove List of [newfloat] from TOC

If you want to do it with \newfloat, here's a way for getting the same functionality of the list printing macros of memoir:

\documentclass[a4paper,twoside]{memoir}
\usepackage{etoolbox}
\usepackage{newfloat}

\makeatletter
%% we define a helper macro for adjusting lists of new floats to
%% accept a * behind them for not being shown in the TOC, like
%% the other list printing commands in memoir
\newcommand{\AdjustForMemoir}[1]{%
  \csletcs{kept@listof#1}{listof#1}%
  \csdef{listof#1}{%
    \@ifstar
     {\csappto{newfloat@listof#1@hook}{\append@star}%
      \csuse{kept@listof#1}}%
     {\csuse{kept@listof#1}}%
  }
}
\def\append@star#1{#1*}
\makeatother

\DeclareFloatingEnvironment{dirfigure}
\AdjustForMemoir{dirfigure} % prepare `\listofdirfigures` so it accepts a *


\begin{document}
\tableofcontents*
\listoffigures*
\listofdirfigures*

\chapter{bah}
\begin{dirfigure}
bah
\caption{bah}
\end{dirfigure}
\begin{figure}
bah
\caption{bah}
\end{figure}
\end{document}

If you use \listofdirfigures without the *, the list will go in the TOC.

This works by exploiting the fact that the last commands executed when \listofdirfigures is called are (in a group)

\newfloat@listofdirfigure@hook\listoffigures

but the newfloat package takes care to redefine things so that \listoffigures will do the right thing. The hook is usually empty, but it's irrelevant. I redefine \listofdirfigures (or better, the alternative version which is called \listofdirfigure) to look for a following *; in this case I append \append@star to the hook, so TeX will eventually see

\append@star\listoffigures

in case \listofdirfigures* is called; this will become \listoffigures* as wanted. In case no * appears, nothing is changed.

I provided an \AdjustForMemoir macro so that every new float list making command can be modified in that way.

For reference, the memoir only way:

\documentclass[a4paper,twoside]{memoir}
\newfloat[chapter]{dirfigure}{dirf}{Dirfigure}
\newlistof{listofdirfigures}{dirf}{List of Dirfigures}
\newlistentry[chapter]{dirfigure}{dirf}{0}
\cftsetindents{dirfigure}{0em}{2.3em}

\begin{document}
\tableofcontents*
\listoffigures*
\listofdirfigures*

\chapter{bah}
\begin{dirfigure}
bah
\caption{bah}
\end{dirfigure}
\begin{figure}
bah
\caption{bah}
\end{figure}
\end{document}