I've taken a shot at checking whether a matter-only, flat FRW model with variable gravitational constant G(t) = G(to) (t / to) can match observations of luminosity distance DL versus redshift z.
As far as I could check, the prediction of the model works quite well:
DL = RH(to) (1 + z) Ln(1 + z)
where RH(to) = c / H(to) is the current Hubble radius, 4222 Mpc for H(to) = 71 km/(s Mpc)
Another advantage of the model is that it is based on setting the Hubble constant H(t) = 1 / t. Therefore it matches current observations that H(to) to = 1.
Details in http://vargfrw.blogspot.com/