We describe an approach for designing high-affinity small molecule-binding proteins poised for downstream sensing. We use deep learning-generated pseudocycles with repeating structural units surrounding central binding pockets with widely varying shapes that depend on the geometry and number of the repeat units. We dock small molecules of interest into the most shape complementary of these pseudocycles, design the interaction surfaces for high binding affinity, and experimentally screen to identify designs with the highest affinity. We obtain binders to four diverse molecules, including the polar and flexible methotrexate and thyroxine. Taking advantage of the modular repeat structure and central binding pockets, we construct chemically induced dimerization systems and low-noise nanopore sensors by splitting designs into domains that reassemble upon ligand addition.