We investigate the phase diagram of the t−J model on a triangular lattice using a variational Monte Carlo approach. We use an extended set of Gutzwiller projected fermionic trial wave functions allowing for simultaneous magnetic and superconducting order parameters. We obtain energies at zero doping for the spin-1∕2 Heisenberg model in very good agreement with the best estimates. Upon electron doping (with a hopping integral t<0) this phase is surprisingly stable variationally up to n≈1.4, while the dx2−y2+idxy order parameter is rather weak and disappears at n≈1.1. For hole doping, however, the coplanar magnetic state is almost immediately destroyed and dx2−y2+idxy superconductivity survives down to n≈0.8. For lower n, between 0.2 and 0.8, we find saturated ferromagnetism. Moreover, there is evidence for a narrow spin density wave phase around n≈0.8. Commensurate flux phases were also considered, but these turned out not to be competitive at finite doping.