The most rapid path to discovering treatment options for the novel coronavirus SARS-CoV-2 is to find existing medications that are active against the virus. We have focused on identifying repurposing candidates for the transmembrane serine protease family member II (TMPRSS2), which is critical for entry of coronaviruses into cells. Using known 3D structures of close homologs, we created seven homology models. We also identified a set of serine protease inhibitor drugs, generated several conformations of each, and docked them into our models. We used three known chemical (non-drug) inhibitors and one validated inhibitor of TMPRSS2 in MERS as benchmark compounds and found six compounds with predicted high binding affinity in the range of the known inhibitors. We also showed that a previously published weak inhibitor, Camostat, had a significantly lower binding score than our six compounds. All six compounds are anticoagulants with significant and potentially dangerous clinical effects and side effects. Nonetheless, if these compounds significantly inhibit SARS-CoV-2 infection, they could represent a potentially useful clinical tool.