We consider the problem of localizing spectrally overlapped sources in cognitive radio networks. A new weighted centroid localization algorithm (WCL) called Cyclic WCL is proposed, which exploits the cyclostationary feature of the target signal to estimate its location coordinates. In order to analyze the algorithm in terms of root-mean-square error (RMSE), we model the location estimates as the ratios of quadratic forms in a Gaussian random vector. With analysis and simulation, we show the impact of the interferer location and its modulation scheme on the RMSE. We also study the RMSE performance of the algorithm for different power levels of the target and the interference. Further, the comparison between Cyclic WCL and WCL w/o cyclostationarity is presented. It is observed that the Cyclic WCL provides significant performance gain over WCL.