In this proceeding we present our theoretical results for the single-diffractive production of open heavy flavor mesons in $pp$ collisions. We estimate that this mechanism constitutes
0.5-2 per cent of the inclusive production of the same mesons in Tevatron and LHC kinematics. In Tevatron kinematics the theoretical expectations are in reasonable agreement with the available experimental data. In LHC kinematics the predicted cross-sections are sufficiently large and could be accessed experimentally. We also analyze the dependence of the cross-sections on multiplicity of co-produced hadrons, and find that it should be significantly lower than that of inclusive production of the same heavy mesons. If confirmed experimentally, this result would corroborate that multiplicity enhancement seen in inclusive production of different quarkonia states is related to multipomeron contributions, rather than other mechanisms.