Spray your centipede grass with a herbicide that is chemically formulated to kill centipede grass, but protect your own preferred grass type. Examples of herbicides that can kill centipede include those that contain diclofop, metribuzin and 2,4-D + triclpyr.
Reapply the herbicide in a few days. Pick a day that is rain- and wind-free to protect your surrounding plants.
Till the areas that contain dead centipede grass. Smooth the top of the bare areas with the back of a rake.
Broadcast your preferred cool or warm season grass seed into the bare areas. Cover the grass seeds with 1/8 inch of compost. Roll a halfway-filled lawn roller over these areas for soil-to-seed contact.
Water the bare areas thoroughly. Keep these areas well watered so your grass seeds will germinate. Lush, new grass will provide competition for the centipede grass, preventing it from coming back.