During the final growth phase of giant planets, accretion is thought to be controlled by a surrounding circumplanetary disc. Current astrophysical accretion disc models rely on hydromagnetic turbulence or gravitoturbulence as the source of effective viscosity within the disc. However, the magnetically coupled accreting region in these models is so limited that the disc may not support inflow at all radii, or at the required rate. Here, we examine the conditions needed for self-consistent accretion, in which the disc is susceptible to accretion driven by magnetic fields or gravitational instability.We model the disc as a Shakura-Sunyaev α disc and calculate the level of ionization, the strength of coupling between the field and disc using Ohmic, Hall and Ambipolar diffusevities for both a magnetorotational instability (MRI) field and vertical field, and the strength of gravitational instability. We find that the standard constant-a disc is only coupled to the field by thermal ionization within 30RJ with strong magnetic diffusivity prohibiting accretion through the bulk of the mid-plane. In light of the failure of the constant-α disc to produce accretion consistent with its viscosity, we drop the assumption of constant-α and present an alternate model in which a varies radially according to the level magnetic turbulence or gravitoturbulence. We find that a vertical field may drive accretion across the entire disc, whereas MRI can drive accretion out to ̃200RJ, beyond which Toomre's Q = 1 and gravitoturbulence dominates. The discs are relatively hot (T ≥ 800 K), and consequently massive (Mdisc ̃ 0.5MJ).