  We study subsets $E$ of finitely generated groups where the set of all words
over a given finite generating set that lie in $E$ forms a context-free
language. We call these sets recognisably context-free. They are invariant of
the choice of generating set and a theorem of Muller and Schupp fully
classifies when the set $\{1\}$ can be recognisably context-free. We extend
Muller and Schupp's result to show that a group $G$ admits a finite
recognisably context-free subset if and only if $G$ is virtually free. We show
that every conjugacy class of a group $G$ is recognisably context-free if and
only if $G$ is virtually free. We conclude by showing that a coset is
recognisably context-free if and only if the Schreier coset graph of the
corresponding subgroup is quasi-isometric to a tree.
