So far as I can tell, here's the list of non-unique Republic (or plausibly available) Jedi-affiliated ships.
J1-Class Interceptor
Jedi-Class Heavy Starfighter
XJ7 StealthX - (I've been informed that after Incom and the Republic parted ways, the Republic returned all the StealthX's it had purchased.)
Eta-6 Delta Interceptor
Expeditionary/Training Ships:
Jocasta-class Light Corvette
Protector-class Corvette
E'ron-class Corvette
Turhaya-class Freighter
Redstar-class Patrol Ship
Skyspirit-class Courier
Major Training Ships:
Kenobi-class Praxeum Ship
Baas-class Training Vessel
Boolon-class Praxeum Ship