Offline Multiplayer Call of Duty Games on Wii: None Exist
No Call of Duty game on Wii offers offline (split-screen/local) multiplayer.
Why
Design Focus: Wii ports prioritized motion controls and online play; local multiplayer was secondary.
Hardware Limits: The Wii's GPU/CPU struggled to render two viewports at playable framerates.
Wii CoD Titles (All Online-Only Multiplayer)
Call of Duty: World at War (2008)
Call of Duty: Modern Warfare Reflex (2009)
Call of Duty: Black Ops (2010)
For split-screen/local multiplayer on Wii, look at other genres: racing (Mario Kart Wii), platformers (New Super Mario Bros. Wii), party games (Wii Party).