Parameters that quantify the acceleration of cosmic expansion are conventionally determined within the standard Friedmann-Lemaître-Robertson-Walker (FLRW) model, which fixes spatial curvature to be homogeneous. Generic averages of Einstein's equations in inhomogeneous cosmology lead to models with non-rigidly evolving average spatial curvature, and different parameterizations of apparent cosmic acceleration. The timescape cosmology is a viable example of such a model without dark energy. Using the largest available supernova data set, the JLA catalogue, we find that the timescape model fits the luminosity distance-redshift data with a likelihood that is statistically indistinguishable from the standard spatially flat ΛCDM cosmology by Bayesian comparison. In the timescape case cosmic acceleration is non-zero but has a marginal amplitude, with best fit apparent deceleration parameter, q0=-0.043+0.004-0.000. Systematic issues regarding standardization of supernova light curves are analysed. Cuts of data at the statistical homogeneity scale affect light curve parameter fits independent of cosmology. A cosmological model dependency of empirical changes to the mean colour parameter is also found. Irrespective of which model ultimately fits better, we argue that as a competitive model with a non-FLRW expansion history, the timescape model may prove a useful diagnostic tool for disentangling selection effects and astrophysical systematics from the underlying expansion history.