  In this paper, we provide an explicit description of the Zariski-open subset
of the moduli space of rank 2 parabolic logarithmic connections in the case
$g\geq 2$. Our approach is to analyze the underlying parabolic bundles and the
apparent singularities of the parabolic connections. We prove that a
Zariski-open subset of the product of a projective space and the moduli space
of parabolic bundles gives a Darboux coordinate for the moduli space of
parabolic connections.
