There are 3 unique codex entries in the Ships section on Coruscant. They are all class specific.
Corellian Defender-class Light Corvette (Consular) | Coordinates: -1256, -4592 | Location: Coruscant: Senate Plaza: Senate Tower
Corellian Defender-class Light Corvette (Knight) | Coordinates: -1308, -4695 | Location: Coruscant: Senate Plaza: Senate Tower
Corellian Defender-class Light Corvette (Knight/Consular) is obtained from speaking with Master Yuon Par during "Ancient Secrets" mission as a Jedi Consular player or General Var Suthra during "Race to the Ruins" mission as a Jedi Knight player.
Codex type: Ships | Faction: Republic | Class: Jedi Consular & Jedi Knight
Associated Achievement: None
Corellian XS Stock Light Freighter (Smuggler) is obtained from speaking with Fabizan during "Race the Devil" mission.
Codex type: Ships | Faction: Republic | Class: Smuggler
Associated Achievement: None
Rendili Hyperworks BT-7 Thunderclap (Trooper) is obtained from speaking with General Garza during "Assault on the Works" mission.
Codex type: Ships | Faction: Republic | Class: Trooper
Associated Achievement: None