This paper considers the problem of finding two-dimensional (2-D) direction of arrivals (DOAs) for coherent cyclostationary signals using a 2-D array with random position errors. To alleviate the performance degradation due to the coherence between the signals of interest (SOIs) and the random perturbation in 2-D array positions, a matrix reconstruction scheme in conjunction with an iterative algorithm is presented to reconstruct the correlation matrices related to the received array data so that the resulting correlation matrices possess the eigenstructures required for finding 2-D DOAs. Then, using the reconstructed matrices, we create a subspace orthogonal to the subspace spanned by the direction vectors of the SOIs. Therefore, the 2-D DOAs of the SOIs can be estimated based on a subspace-fitting concept and the created subspace. Finally, several simulation examples are presented for illustration and comparison.