Greek letters wiith continuing circumflex

This is font related: In a Unicode fonts, the accents are mostly placed using so called anchors: Every character has a special position marked in the font file, such that a marked position of the accent is aligned with this "anchor". The font designers did not add these anchors to greek letters.

Of course you could fix this by adding the anchors yourself, but if you only need this in rare situation and only with small characters, you can just position the accent manually. Most of the time you just need \llap to place the accent over the next character and sometimes you have to \raise it too. For example:

\documentclass{article}
\usepackage{fontspec} 
\setmonofont{DejaVuSansMono.ttf}
\begin{document}
\texttt{â \quad b̂ \quad ĉ \quad \llap{̂}α \quad \raisebox{2pt}{\llap{̂}}β \quad \llap{̂}γ \quad \llap{̇}α \quad \raisebox{2pt}{\llap{̇}}β \quad \llap{̇}γ}
\end{document}