This paper introduces a new score-informed method for the segmentation of jingju a cappella singing phrase into syllables. The proposed method estimates the most likely sequence of syllable boundaries given the estimated syllable onset detection function (ODF) and its score. Throughout the paper, we first examine the jingju syllables structure and propose a definition of the term "syllable onset". Then, we identify which are the challenges that jingju a cappella singing poses. Further, we investigate how to improve the syllable ODF estimation with convolutional neural networks (CNNs). We propose a novel CNN architecture that allows to efficiently capture different time-frequency scales for estimating syllable onsets. In addition, we propose using a score-informed Viterbi algorithm -instead of thresholding the onset function-, because the available musical knowledge we have (the score) can be used to inform the Viterbi algorithm in order to overcome the identified challenges. The proposed method outperforms the state-of-the-art in syllable segmentation for jingju a cappella singing. We further provide an analysis of the segmentation errors which points possible research directions.