Using deep, high-spatial-resolution imaging from the Hubble Space Telescope/Advanced Camera for Surveys (HST/ACS) Coma Cluster Treasury Survey, we determine colour profiles of early-type galaxies in the Coma cluster. From 176 galaxies brighter than MF814W(AB)=-15mag that are either spectroscopically confirmed members of Coma or identified by eye as likely members from their low surface brightness, data are provided for 142 early-type galaxies. Typically, colour profiles are linear against log (R), sometimes with a nuclear region of distinct, often bluer colour associated with nuclear clusters. Colour gradients are determined for the regions outside the nuclear components. We find that almost all colour gradients are negative, both for elliptical and for lenticular galaxies. Most likely, earlier studies that report positive colour gradients in dwarf galaxies are affected by the bluer colours of the nuclear clusters, underlining that high-resolution data are essential to disentangle the colour properties of the different morphological components in galaxies. Colour gradients of dwarf galaxies form a continuous sequence with those of elliptical galaxies, becoming shallower towards fainter magnitudes. Interpreting the colours as metallicity tracers, our data suggest that dwarfs as well as giant early-type galaxies in the Coma cluster are less metal rich in their outer parts. We do not find evidence for environmental influence on the gradients, although we note that most of our galaxies are found in the central regions of the cluster. For a subset of galaxies with known morphological types, S0 galaxies have less steep gradients than elliptical galaxies.