Neutron-rich silver isotopes were populated in the fragmentation of a 136Xe beam and the relativistic fission of 238U. The fragments were mass analyzed with the GSI Fragment Separator and subsequently implanted into a passive stopper. Isomeric transitions were detected by 105 high-purity germanium detectors. Eight isomeric states were observed in 122-126Ag nuclei. The level schemes of 122,123,125Ag were revised and extended with isomeric transitions being observed for the first time. The excited states in the odd-mass silver isotopes are interpreted as core-coupled states. The isomeric states in the even-mass silver isotopes are discussed in the framework of the proton-neutron split multiplets. The results of shell-model calculations, performed for the most neutron-rich silver nuclei are compared to the experimental data.