Thermoacoustic instability is a serious issue in practical combustion systems. Such systems are inherently noisy, and hence the influence of noise on the dynamics of thermoacoustic instability is an aspect of practical importance. The present work is motivated by a recent report on the experimental observation of coherence resonance, or noise-induced coherence with a resonance-like dependence on the noise intensity as the system approaches the stability margin, for a prototypical premixed laminar flame combustor (Kabiraj et al., Phys. Rev. E, 4 (2015)). We numerically investigate representative thermoacoustic models for such noise-induced dynamics. Similar to the experiments, we study variation in system dynamics in response to variations in the noise intensity and in a critical control parameter as the systems approach their stability margins. The qualitative match identified between experimental results and observations in the representative models investigated here confirms that coherence resonance is a feature of thermoacoustic systems. We also extend the experimental results, which were limited to the case of subcritical Hopf bifurcation, to the case of supercritical Hopf bifurcation. We identify that the phenomenon has qualitative differences for the systems undergoing transition via subcritical and supercritical Hopf bifurcations. Two important practical implications are associated with the findings. Firstly, the increase in noise-induced coherence as the system approaches the onset of thermoacoustic instability can be considered as a precursor to the instability. Secondly, the dependence of noise-induced dynamics on the bifurcation type can be utilised to distinguish between subcritical and supercritical bifurcation prior to the onset of the instability. (C) 2016 Elsevier Ltd. All rights reserved.