This paper presents a novel framework for super-resolution direction of arrival (DOA) estimation of acoustic sources in the spherical harmonics (SH) domain. The proposed approach combines sparse Bayesian learning (SBL) with a convolutional neural network (CNN). The CNN is utilized to classify DOA based on the spherical harmonics decomposition (SHD) of recordings from a spherical microphone array (SMA), providing coarse DOA estimates. These estimates are then refined using SBL, which operates on a densely sampled grid around the CNN-predicted DOA classes to achieve precise localization. The CNN component exhibits robustness in noisy and reverberant environments, while SBL specializes in high-resolution localization of multiple sparse sources. By leveraging the strengths of both methods, the SH-CNN-SBL framework enhances DOA estimation accuracy in challenging conditions. Extensive simulations and real-world experiments are performed to validate the effectiveness, of the proposed method in achieving a resolution of 1◦