We have carried out theoretical studies on Ising-type endohedral fullerene (EF) structure with a dopant magnetic atom encaged within the diluted magnetic spherical cage to examine the evolution in magnetic behaviors. We show how the thermal behaviors and phase diagrams of Ising-type EF are affected by diluted surface, crystal field and exchange couplings. We have used to investigate theoretically the effect of Hamiltonian parameters the effective field calculations within Ising model framework. The model Hamiltonian includes nearest neighbor ferromagnetic and antiferromagnetic center-surface (C-S) interaction as well as ferromagnetic surface interaction. We have shown that the system exhibits the first and second order phase transitions as well as tricritical point. In particular, the conditions for the occurrence of these reentrant and double reentrant behaviors are given explicitly.