Only two Call of Duty games released on PlayStation 2:
Call of Duty: Finest Hour (2004) – Developed by Spark Unlimited. Standalone campaign (Eastern Front, North Africa, Battle of the Bulge). No multiplayer on PS2 (online was PC-only). Not part of the main COD timeline.
Call of Duty 2 (2005) – Port of the PC/360 game by Treyarch. Single-player only (no split-screen, no online). Reduced graphics, missing missions vs. 360/PC.
Not on PS2
Call of Duty (2003) – PC only.
Call of Duty 3 (2006) – PS3, Wii, Xbox 360, PS2 cancelled late in dev.
Modern Warfare series, Black Ops, etc. – PS3/360/PC onward.
If you want the classic WWII COD experience on PS2, Finest Hour is unique; COD 2 is a stripped port. Both are playable but show the hardware's limits.