The magnetic phase transition of a two-dimensional (2D) random spin system with competing exchange interactions, stage-2 GICs, has been studied using SQUID AC magnetic susceptibility and SQUID DC magnetization. The magnetic phase diagram of critical temperature versus Cu concentration is determined. For the system undergoes two phase transitions at and . Below a 2D ferromagnetic order is established in each intercalate layer. Below there appears a 3D antiferromagnetic phase with the 2D ferromagnetic layers being antiferromagnetically coupled along the c-axis. For the system undergoes a phase transition at and a reentrant spin glass transition at . For the system undergoes a spin glass transition at from the paramagnetic phase to the spin glass phase. No phase transition is observed for c = 1 at least above 0.3 K because of the fully frustrated nature of the 2D antiferromagnet on the triangular lattice. The enhancement of in the intermediate concentration and the positive sign of the Curie-Weiss temperature for c < 0.83 indicates that the intraplanar interaction between and spins is ferromagnetic. The nature of the ferromagnetic phase, reentrant spin glass phase and spin glass phase is examined from the frequency dependence of absorption .