Greek diacritic with English letter

You can use the accents provided by the LGR encoding:

\documentclass{article}
\usepackage[LGR,T1]{fontenc} % or OT1

\DeclareTextAccentDefault{\accdialytika}{LGR}
\DeclareTextAccentDefault{\acctonos}{LGR}
\DeclareTextAccentDefault{\accdasia}{LGR}
\DeclareTextAccentDefault{\accpsili}{LGR}
\DeclareTextAccentDefault{\accvaria}{LGR}
\DeclareTextAccentDefault{\accperispomeni}{LGR}
\DeclareTextAccentDefault{\accdialytikaperispomeni}{LGR}
\DeclareTextAccentDefault{\accdialytikatonos}{LGR}
\DeclareTextAccentDefault{\accdasiaperispomeni}{LGR}
\DeclareTextAccentDefault{\accdasiavaria}{LGR}
\DeclareTextAccentDefault{\accdasiaoxia}{LGR}
\DeclareTextAccentDefault{\accpsiliperispomeni}{LGR}
\DeclareTextAccentDefault{\accpsilioxia}{LGR}
\DeclareTextAccentDefault{\accpsilivaria}{LGR}
\DeclareTextAccentDefault{\accinvertedbrevebelow}{LGR}
\DeclareTextAccentDefault{\accbrevebelow}{LGR}

\begin{document}

\accdialytika{x}
\acctonos{x}
\accdasia{x}
\accpsili{x}
\accvaria{x}
\accperispomeni{x}
\accdialytikaperispomeni{x}
\accdialytikatonos{x}
\accdasiaperispomeni{x}
\accdasiavaria{x}
\accdasiaoxia{x}
\accpsiliperispomeni{x}
\accpsilioxia{x}
\accpsilivaria{x}
\accinvertedbrevebelow{x}
\accbrevebelow{x}

\end{document}

Pick the ones you need. You may also do \newcommand{\rb}[1]{\accdasia{#1}} so you can simply type \rb{x}.

If you need the dasia in math mode, it's even simpler:

\documentclass{article}
\usepackage[LGR,T1]{fontenc} % or OT1

\DeclareSymbolFont{greekletters}{LGR}{\familydefault}{m}{n}
% lgrenc.def has
% \DeclareTextAccent{\accdasia}{LGR}{60} % δασεῖα spiritus asper (rough breathing)
\DeclareMathAccent{\rb}{\mathord}{greekletters}{60}

\begin{document}

$\rb{x}$

\end{document}

Maybe something like this?

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[polutonikogreek,english]{babel}
\usepackage{tipa}

\usepackage{stackengine,graphicx}
\newcommand\rb[1]{\stackengine{1pt}{#1}{\scalebox{-1}[.7]{\reflectbox{$\scriptscriptstyle
  \prime$}\kern-1pt\raisebox{2pt}{,}}}{O}{c}{F}{F}{S}}
\begin{document}
{\greektext{<'otan}}

\rb x\greektext{tan}
\end{document}