Singing voice beat tracking is a challenging task, due to the lack of musical accompaniment that often contains robust rhythmic and harmonic patterns, something most existing beat tracking systems utilize and can be essential for estimating beats. In this paper, a novel temporal convolutional network-based beat-tracking approach featuring self-supervised learning (SSL) representations and adapter tuning is proposed to track the beat and downbeat of singing voices jointly. The SSL DistilHuBERT representations are utilized to capture the semantic information of singing voices and are further fused with the generic spectral features to facilitate beat estimation. Sources of variabilities that are particularly prominent with the non-homogeneous singing voice data are reduced by the efficient adapter tuning. Extensive experiments show that feature fusion and adapter tuning improve the performance individually, and the combination of both leads to significantly better performances than the un-adapted baseline system, with up to 31.6% and 42.4% absolute F1-score improvements on beat and downbeat tracking, respectively.