  A microscopic theory of the electronic spectrum and of superconductivity
within the t-J model on the honeycomb lattice is developed. We derive the
equations for the normal and anomalous Green functions in terms of the Hubbard
operators by applying the projection technique. Superconducting pairing of d +
id'-type mediated by the antiferromagnetic exchange is found. The
superconducting Tc as a function of hole doping exhibits a two-peak structure
related to the van Hove singularities of the density of states for the two-band
t-J model. At half-filling and for large enough values of the exchange
coupling, gapless superconductivity may occur. For small doping the coexistence
of antiferromagnetic order and superconductivity is suggested. It is shown that
the s-wave pairing is prohibited, since it violates the constraint of
no-double-occupancy.
