  We update the allowed parameter space of the CP-violating 2HDM with Type II
Yukawa couplings, that survives the current experimental and theoretical
constraints on the model. For a representative set of allowed parameter points,
we study the production of charged Higgs bosons, both at the LHC at 14 TeV and
at a possible future hadronic collider at 30 TeV. Two classes of production
mechanisms are considered, "bosonic" (pp\to H^\pm W^\mp X) and "fermionic" (pp
\to H^+ \bar t (b) X). After commenting on our previous H^\pm\to W^\pm H_1
investigation, we focus on the tauonic decay mode, H^\pm \to \tau\nu,
performing a detailed signal-over-background analysis at the parton level. The
increased features provided when considering CP violation, i.e., the extension
of the parameter space and the mixing of the would-be CP-odd scalar boson, only
marginally increase the discovery prospects, which remain very challenging both
when increased luminosities and higher energies are considered.
