James Corden has at least 2 NYC restaurant owners in his corner ... they say he's been a model customer, despite some alleged nasty behavior at other establishments. While James was briefly banned at Big Apple hotspot Balthazar, the owner of some of NYC's top restaurants tells us JC was always…

Celebrity chef/restaurateur Todd English has 2 problems ... he's being sued for not paying his massive food bill ... and he serves FROZEN rabbit. Greentree Packing claims in a new lawsuit -- obtained by TMZ -- English agreed to buy $73K worth of unprepared food items ... for his famed Olives…