We present a new analysis of the early-type galaxy population in the central region of the Antlia cluster, focusing on the faint systems such as dwarf ellipticals (dEs) and dwarf spheroidals (dSphs). The colourmagnitude relation (CMR) and the relation between luminosity and mean effective surface brightness for galaxies in the central region of Antlia have been previously studied in Paper I of the present series. Now we confirm 22 early-type galaxies as Antlia members, using Gemini-GMOS and Magellan-MIKE spectra. Among them, 15 are dEs from the FS90 Antlia Group catalogue, two belong to the rare type of compact ellipticals (cEs) and five are new faint dwarfs that had never been catalogued before. In addition, we present 16 newly identified low-surface-brightness galaxy candidates, almost half of them displaying morphologies consistent with being Antlias counterparts of Local Group dSphs, which extend the faint luminosity limit of our study down to MB=-10.1(BT= 22.6) mag. With these new data, we built an improved CMR in the Washington photometric system, i.e. integrated T1 magnitudes versus (C-T1) colours, which extends similar to 4 mag faintwards the limit of spectroscopically confirmed Antlia members. When only confirmed early-type members are considered, this relation extends over 10 mag in luminosity with no apparent change in slope or increase in colour dispersion towards its faint end. The intrinsic colour scatter of the relation is compared with those reported for other clusters of galaxies; we argue that it is likely that the large scatter of the CMR, usually reported at faint magnitudes, is mostly due to photometric errors along with an improper membership/morphological classification. The distinct behaviour of the luminosity versus mean effective surface brightness relation at the bright and faint ends is analysed, while it is confirmed that dE galaxies on the same relation present a very similar effective radius, regardless of their colour. The projected spatial distribution of the member sample confirms the existence of two groups in Antlia, each one dominated by a giant elliptical galaxy and with one cE located close to each giant. Size and position, with respect to massive galaxies, of the dSph candidates are estimated and compared to Local Group counterparts.