Abstract Quasi-static aberrations in coronagraphic systems are the ultimate limitation to the capabilities of exoplanet imagers both ground-based and space-based. These aberrations – which can be due to various causes such as optics alignment or moving optical parts during the observing sequence – create light residuals called speckles in the focal plane. Those speckles might be mistaken for planets. For ground-based instruments, the presence of residual turbulent wavefront errors due to partial adaptive optics correction causes an additional difficulty to the challenge of measuring aberrations in the presence of a coronagraph. In this paper, we present an extension of COFFEE, the coronagraphic phase diversity, to the estimation of quasi-static aberrations in the presence of adaptive-optics-corrected residual turbulence. We perform realistic numerical simulations to assess the performance that can be expected on an instrument of the current generation. We perform the first experimental validation in the laboratory, which demonstrates that quasi-static aberrations can be corrected during the observations by means of coronagraphic phase diversity.