This paper proposes two subspace-based methods for direction-of-arrival (DOA) estimation of coherent signals for uniform linear arrays (ULAs) with unknown mutual coupling. Based on the banded symmetric Toeplitz structure of the mutual coupling matrix (MCM), the conventional spatial smoothing method can be exploited for DOA estimation of coherent signals. We firstly study a new scheme with spatial smoothing on the middle subarray, which can be considered as an ideal array without uncertainties based on the special property of mutual coupling of ULAs. Next, an alternative method with larger effective antenna aperture is proposed. Unlike the first method, the latter one smoothes on the whole array instead of the middle subarray and a better performance is achieved. Numerical examples are given to illustrate the performance of these two algorithms for coherent DOA estimation in the presence of mutual coupling.