We present scaling relations between structural properties of nuclear star clusters and their host galaxies for a sample of early-type dwarf galaxies observed as part of the Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) Coma Cluster Survey. We have analysed the light profiles of 200 early-type dwarf galaxies in the magnitude range 16.0<m_F814W_<22.6mag, corresponding to -19.0<M_F814W_<-12.4mag. Nuclear star clusters are detected in 80 percent of the galaxies, thus doubling the sample of HST-observed early-type dwarf galaxies with nuclear star clusters. We confirm that the nuclear star cluster detection fraction decreases strongly towards faint magnitudes. The luminosities of nuclear star clusters do not scale linearly with host galaxy luminosity. A linear fit yields L_nuc_~L_gal_^0.57^+/-0.05. The nuclear star cluster-host galaxy luminosity scaling relation for low-mass early-type dwarf galaxies is consistent with formation by globular cluster (GC) accretion. We find that at similar luminosities, galaxies with higher Sersic indices have slightly more luminous nuclear star clusters. Rounder galaxies have on average more luminous clusters. Some of the nuclear star clusters are resolved, despite the distance of Coma. We argue that the relation between nuclear star cluster mass and size is consistent with both formation by GC accretion and in situ formation. Our data are consistent with GC inspiralling being the dominant mechanism at low masses, although the observed trend with Sersic index suggests that in situ star formation is an important second-order effect.