An experimentally feasible configuration of a prism coupler with an electromagnetically-induced-transparency (EIT) medium layer, e.g., a semiconductor-quantum-dot (SQD) medium, deposited upon its prism base is suggested for generating tunable surface-plasmon-polariton resonance. Such surface-plasmon-polariton resonance and optical excitation of a surface plasmon wave can be manipulated by switchable quantum interference among SQD multilevel transitions driven by two external control fields. When an incident probe field is coupled into a surface plasmon wave excitation mode, the surface-plasmon-polariton (SPP) resonance at the interface between the SQD medium layer and the substrate will arise, and the quantum-coherently controllable reflection spectrum of the probe field on the prism base can be achieved. In this process, destructive and constructive quantum interference (determined by the intensity ratio of the two external control fields) in the SQD multilevel system plays a key role for achieving the tunable reflection spectrum. The EIT-based surface-plasmon-polariton resonance presented here will have three characteristics (some of them would be attractive): (i) switchable quantum interference exhibited by surface plasmon wave excitation, (ii) quantum-coherently controllable surface plasmon polaritons by external optical fields, (iii) surface wave sensitive to dispersion of the SQD quantum coherent medium. Such an effect of controllable optical response based on the quantum-interference switchable surface-plasmon-polariton resonance in the EIT-prism coupler may find some potential applications in design of new photonic and quantum optical devices.