> You can use “way=byhead” to reset the counter with each section.
It does not work (with ConTeXt ver: 2012.05.30):
\defineenumeration[cool][text=Cool, way=byhead]
\starttext
\section{Cat}
\subsection{Cat}
\cool{}
\cool{}
\subsection{Cat}
\cool{}
\cool{}
\section{Cat}
\cool{}
\cool{}
Hello world!
\stoptext