We develop an approach to generate finite-range atomic interactions via optical Rydberg-state excitation and study the underlying excitation dynamics in theory and experiment. In contrast to previous work, the proposed scheme is based on resonant optical driving and the establishment of a dark state under conditions of electromagnetically induced transparency (EIT). Analyzing the driven dissipative dynamics of the atomic gas, we show that the interplay between coherent light coupling, radiative decay, and strong Rydberg-Rydberg atom interactions leads to the emergence of sizable effective interactions while providing remarkably long coherence times. The latter are studied experimentally in a cold gas of strontium atoms for which the proposed scheme is most efficient. Our measured atom loss is in agreement with the theoretical prediction based on binary effective interactions between the driven atoms.