Two series of new green phosphorescent polymers bearing a bis(2-phenyl-pyridine)iridium(III)(dibenzoylmethane) [$(ppy)_2Irdbm$] complex were designed and synthesized. Poly-carbazole (PCbz) derivative or polyfluorene with pendant carbazole groups (PFCbz) were employed as host polymers for the iridium complex. The iridium complex monomer was copolymerized with the host monomers using varying monomer ratios via a Yamamoto coupling reaction. Efficient energy transfer from host to dopant unit was observed by increasing the ratio of the iridium guest in the copolymers. Electroluminescent devices with the configuration ITO/PEDOT:PSS/polymer/BmPyPB/LiF/Al were fabricated and characterized. The phosphorescent polymers composed of the iridium complex guest and polyfluorene with carbazole pendants as a host performed better than the polymers composed of the same guest and the main chain polycarbazole host. A maximum external quantum efficiency of 0.73%, a luminous efficiency of 1.21 cd/A, and a maximum luminance of 372 $cd/m^2$ were obtained from a device fabricated using one of the synthesized copolymers.