I'd say the problem with the Rhodamines is that oxygen molecule right in the middle of the molecule. The cyanines have carbon atoms that are conjugated (google it) between the nitrogens. It's that conjugation that allows the dye to have electron resonance and be good dye. The oxygens don't allow the resonance as well being in the middle of the chain of conjugated carbons.
I believe (PE correct me if I get it wrong) it's the electron orbitals projecting up from the nitrogens on the ends of the cyanines are the source of the electrons for the resonance and also allow the dye to attach to the silver halide crystal.