We report on a detailed investigation of the itinerant ferromagnets LaCoAsO, PrCoAsO and SmCoAsO performed by means of muon spin spectroscopy upon the application of external hydrostatic pressures p up to 2.4 GPa. These materials are shown to be magnetically hard in view of the weak dependence of both critical temperatures T C and internal fields at the muon site on p. In the cases R=La and Sm, the behaviour of the internal field is substantially unaltered up to p=2.4 GPa. A much richer phenomenology is detected in PrCoAsO instead, possibly associated with a strong p dependence of the statistical population of the two different crystallographic sites for the muon. Surprisingly, results are notably different from what is observed in the case of the isostructural compounds RCoPO, where the full As/P substitution is leading to smaller values of unit cell volume already at ambient pressure but p is still very effective in further affecting the magnetic properties.