Page numbers vertically centered in the outer page margin

You can use the background package; a little exampe:

\documentclass[twoside]{scrbook}
\usepackage{background}
\usepackage{ifthen}
\usepackage{lipsum}

\SetBgContents{}
\SetBgAngle{0}
\SetBgColor{black}
\SetBgScale{3}

\makeatletter
\AddEverypageHook{%
  \ifthenelse{\isodd{\value{page}}}%
  {\SetBgPosition{1.05\textwidth,-.5\textheight}}
  {\SetBgPosition{0.3,-.5\textheight}}
  \SetBgContents{-\thepage-}
  \bg@material%
}
\makeatother

\pagestyle{empty}

\begin{document}
\lipsum[1-30]
\end{document}

Another solution with only KOMA-Script tools (and some low level trickery):

\usepackage{scrpage2}
\pagestyle{scrheadings}
\setlength{\footskip}{0pt}
\rofoot[\centerpageno{o}]{\centerpageno{o}}
\lefoot[\centerpageno{e}]{\centerpageno{e}}
\def\centerpageno#1{\leavevmode
  \vbox to 0pt{
    \vss
    \hbox to 0pt{\Huge\normalfont
      \if#1o\kern 2em\else\hss\fi\thepage
      \if#1o\hss\else\kern2em\fi}
    \vskip.5\textheight
    \vskip\baselineskip}}

I use the normal footer, putting into it a zero height box that contains a zero width box that is raised to the center of the text block; in it the page number is typeset shifted on the right or on the left depending if we are in an odd or even page.

You could also use KOMA-Script package scrlayer-scrpage. It is the successor of the deprecated package scrpage2.

scrlayer-scrpage uses layer to declare pagestyles. So you can declare a new layer for the pagenumber in the outer margin and add this layer to pagestyle scrheadings and plain.scrheadings. Note that after loading scrlayer-scrpage pagestyle scrheadings is set and pagestyle plain is redefined as an aliaspagestyle for plain.scrheadings.

\documentclass{scrbook}
\usepackage[automark]{scrlayer-scrpage}
\clearpairofpagestyles
\ohead{\headmark}

\DeclareNewLayer[
  background,
  outermargin,
  height=\textheight,
  voffset=1in+\voffset+\topmargin+\headheight+\headsep,
  contents={%
    \vfill
    \ifodd\value{page}\hspace*{.4\layerwidth}\else\hfill\fi
    \pagemark
    \ifodd\value{page}\else\hspace*{.4\layerwidth}\fi
    \vfill
  }
]{outermargin.pagenumber}
\AddLayersToPageStyle{scrheadings}{outermargin.pagenumber}
\AddLayersToPageStyle{plain.scrheadings}{outermargin.pagenumber}

\addtokomafont{pagenumber}{\Huge}

\usepackage{blindtext}% <- only for dummy text
\begin{document}
\chapter{Fruits}
\section{Bananas}
\Blindtext[20]
\end{document}

results in