The recent development of highly sensitive solid-state detectors such as Skipper CCDs has achieved single-electron event resolution, allowing the search for rare interactions with an energy threshold as low as 1.2 eV. In addition, models of dark matter (DM) with masses of a few (1-5) MeV interacting with electrons predict a diurnal modulation of single-electron events in such detectors. This modulation would be enhanced in the southern hemisphere because the DM wind comes from 40 degrees north. The DM$^2$ experiment aims to probe this region of the parameter space in Bariloche, southern Argentina, and has been recently upgraded with a 3g prototype Skipper CCD. The CONNIE experiment uses two Skipper CCDs to search for CEvNS with nuclear reactor neutrinos, but it can also probe dark matter models in the aforementioned region of the parameter space. In this paper, a short description of the expected diurnal modulation of DM is given. Current status, data, results and future perspectives for DM searches in both experiments are discussed.