Inhibitors of the protein-protein interaction (PPI) between the SARS-CoV-2 spike protein and ACE2, which acts as a ligand-receptor pair that initiates the viral attachment and cellular entry of this coronavirus causing the ongoing COVID-19 pandemic, are of considerable interest as potential antiviral agents. While blockade of such PPIs with small molecules is more challenging than with antibodies, small-molecule inhibitors (SMIs) might offer alternatives that are less strain- and mutation-sensitive, suitable for oral or inhaled administration, and more controllable / less immunogenic. Here, we report the identification of SMIs of this PPI by screening our compound-library that is focused on the chemical space of organic dyes. Among promising candidates identified, several dyes (Congo red, direct violet 1, Evans blue) and novel drug-like compounds (DRI-C23041, DRI-C91005) inhibited the interaction of hACE2 with the spike proteins of SARS-CoV-2 as well as SARS-CoV with low micromolar activity in our cell-free ELISA-type assays (IC50s of 0.2-3.0 μM); whereas, control compounds, such as sunset yellow FCF, chloroquine, and suramin, showed no activity. Protein thermal shift assays indicated that the SMIs identified here bind SARS-CoV-2-S and not ACE2. Selected promising compounds inhibited the entry of a SARS-CoV-2-S expressing pseudovirus into ACE2-expressing cells in concentration-dependent manner with low micromolar IC50s (6-30 μM). This provides proof-of-principle evidence for the feasibility of small-molecule inhibition of PPIs critical for coronavirus attachment/entry and serves as a first guide in the search for SMI-based alternative antiviral therapies for the prevention and treatment of diseases caused by coronaviruses in general and COVID-19 in particular.