Stochastic resonance (SR) in a two-coupled oscillator system with time delay is investigated. The system shows multistability of a desynchronized state and two synchronized states with different collective frequencies, which may be interpreted as multistable perception of ambiguous or reversible figures. To model the situations where the two oscillators exist in different environments, periodic signals and noises at their inputs are not uniformly given. SR in an individual oscillator, characterized by the output signal-to-noise ratio, is examined based on numerical simulations. We find that phase shift between the signals at inputs of different oscillators weakens SR, the oscillator with only an input signal does not show SR, and the oscillator with input noise shows SR irrespective of it having an input signal or not. The results have implications in the area of information transmission in biological systems.