Direction-of-Arrival (DOA) estimation in the presence of coherent sources remains a challenging problem in array signal processing, particularly when dealing with rank-deficient covariance matrices due to limited snapshots. The reason behind this difficulty is primarily because coherent (i.e., highly correlated or multipath) sources make the sample covariance matrix rank-deficient, especially when there are limited snapshots or low Signal-to-Noise Ratios (SNRs). Thus, conventional subspace-based DOA estimation techniques such as MUSIC and ESPRIT fail to accurately estimate the angles of arrival since these methods are derived from the full-rank covariance matrix assumption and the uncorrelated sources' assumption. Additionally, techniques such as spatial smoothing, which are commonly used to deal with coherence, introduce additional computational complexity and reduce angular resolution. These limitations point to the significance of developing more robust and resilient methods that would be capable of maintaining a high-resolution DOA estimation under actual source coherence, low SNR, and sparsity levels of available data. This paper presents a novel adaptive sparse regularization framework that effectively addresses these challenges through three key innovations. First, an adaptive regularization scheme automatically adjusts to signal conditions. Second, a sparse weighting mechanism enhances the resolution for coherent sources. Finally, a computationally efficient implementation is suitable for real-time applications. The theoretical analysis establishes a modified Cramér-Rao Lower Bound that accounts for both coherent sources and regularization effects. Extensive simulations demonstrate that the proposed method achieves superior performance compared to existing approaches, with RMSE improvements of up to 40% under low SNR conditions (-20 to -15 dB) compared to traditional MUSIC, ESPRIT, and regularized least-squares methods. The method maintains robust performance even with coherent sources, achieving angular accuracy within 0.4° at high SNRs, while requiring computational complexity comparable to existing techniques. These results establish this approach as a practical solution to challenging DOA estimation scenarios in real-world applications.