We provide compelling numerical evidence of deterministic coherence and anti-coherence resonance in small networks of unidirectional coupled chaotic Rössler oscillators in star and star-ring configurations in the presence of a small mismatch between natural frequencies of the oscillators. The resonance phenomena are found in both the normalized standard deviations of the peak amplitude and inter-peak time interval with respect to the coupling strength and frequency mismatch. The deterministic coherence/anti-coherence resonance resembles self-stabilization/destabilization of the network when the coupling makes collective dynamics more regular/irregular.