  We compare the cosmology of conformal gravity (CG), (Mannheim 2006), to
$\Lambda$CDM. CG cosmology has repulsive matter and radiation on cosmological
scales, while retaining attractive gravity at local scales. Mannheim (2003)
finds that CG agrees with $\Lambda$CDM for supernova data at redshifts $z<1$.
We use GRBs and quasars as standard candles to contrast these models in the
redshift range $0<z<8$. We find CG deviates significantly from $\Lambda$CDM at
high redshift and that $\Lambda$CDM is favoured by the data with
$\Delta\chi^2=48$. Mannheim's model has a bounded dark energy contribution, but
we identify a $\lambda$ fine-tuning problem and a cosmic coincidence problem.
