Antirelaxation coatings in atomic vapor cells allow ground-state coherent spin states to survive many collisions with the cell walls. This reduction in the ground-state decoherence rate gives rise to ultranarrow-bandwidth features in electromagnetically induced transparency (EIT) spectra, which can form the basis of, for example, long-time scale slow and stored light, sensitive magnetometers, and precise frequency standards. Here we study, both experimentally and theoretically, how Zeeman EIT contrast and width in paraffin-coated rubidium vapor cells are determined by cell and laser-beam geometry, laser intensity, and atomic density. Using a picture of Ramsey pulse sequences, where atoms alternately spend ``bright'' and ``dark'' time intervals inside and outside the laser beam, we explain the behavior of EIT features in coated cells, highlighting their unique characteristics and potential applications.