Direction-of-arrival (DOA) estimation is an important step in acoustic scene analysis. Multiple signal classification in the eigenbeam domain (EB-MUSIC) is an accurate direction-of-arrival (DOA) estimation method for rigid spherical microphone arrays. Two important issues with this method are 1) the requirement of prior information about the number of coherent source components, and 2) its computational cost. In this paper, a computationally efficient two-stage method, which can alleviate these problems, is proposed. The proposed method is robust to reverberation, and can be used to efficiently localize multiple coherent sources. An evaluation of the method using simulated recordings under highly reverberant conditions is also presented.