We consider the source coding problem of a binary discrete memoryless source with correlated side information available only at the receiver whose conditional distribution given the source is unknown to the encoder. We propose two methods based on polar codes to attain the achievable rates under this setting. The first method incorporates a staircase scheme, which has been used for universal polar coding for a compound channel. The second method is based on the technique of universalization using bit-channel combining. We also give a list of pros and cons for the two proposed methods.