Encoding correlated sources at separate encoders has been studied extensively from the perspective of asymptotically long block codes. The associated error exponents are known for the case of lossless source coding. In this paper, we introduce a novel technique for deriving achievable error exponents for lossy source coding problems, where the original sources need to be reconstructed to within some fidelity. its an example, we show how to apply our technique to determine achievable error exponents for the Berger-Yeung problem.