  In this work we analyze kinematical conformal cosmology (KCC), an alternative
cosmological model based on conformal Weyl gravity (CG), and test it against
current type Ia supernova (SNIa) luminosity data and other astrophysical
observations. Expanding upon previous work on the subject, we revise the
analysis of SNIa data, confirming that KCC can explain the evidence for an
accelerating expansion of the Universe without using dark energy or other
exotic components. We obtain an independent evaluation of the Hubble constant,
H_{0} = 67.53 km/s Mpc, very close to the current best estimates. The main KCC
and CG parameters are re-evaluated and their revised values are found to be
close to previous estimates. We also show that available data for the Hubble
parameter as a function of redshift can be fitted using KCC and that this model
does not suffer from any apparent age problem. Overall, KCC remains a viable
alternative cosmological model, worthy of further investigation.
