Does galaxy evolution proceed through the green valley via multiple pathways or as a single population? Motivated by recent results highlighting radically different evolutionary pathways between early- and late-type galaxies, we present results from a simple Bayesian approach to this problem wherein we model the star formation history (SFH) of a galaxy with two parameters, [t, τ] and compare the predicted and observed optical and near-ultraviolet colours. We use a novel method to investigate the morphological differences between the most probable SFHs for both disc-like and smooth-like populations of galaxies, by using a sample of 126 316 galaxies (0.01 < z < 0.25) with probabilistic estimates of morphology from Galaxy Zoo. We find a clear difference between the quenching time-scales preferred by smooth- and disc-like galaxies, with three possible routes through the green valley dominated by smooth- (rapid time-scales, attributed to major mergers), intermediate- (intermediate time-scales, attributed to minor mergers and galaxy interactions) and disc-like (slow time-scales, attributed to secular evolution) galaxies. We hypothesize that morphological changes occur in systems which have undergone quenching with an exponential time-scale τ < 1.5 Gyr, in order for the evolution of galaxies in the green valley to match the ratio of smooth to disc galaxies observed in the red sequence. These rapid time-scales are instrumental in the formation of the red sequence at earlier times; however, we find that galaxies currently passing through the green valley typically do so at intermediate time-scales.