Dead Island does not support split-screen multiplayer on PlayStation 3. The game features cooperative gameplay, but it's strictly limited to online multiplayer. There is no local co-op or split-screen functionality on this platform.
If you want to play with a friend locally, you'll need two consoles, two copies, and an internet connection (or LAN via system link, if supported). For couch co-op zombie action, consider Dead Island 2 (PS4/PS5) or Dying Light 2—neither support split-screen either, but Back 4 Blood and World War Z offer online co-op with larger player counts.