No direct train between Kochi & Rameswaram.
First travel upto Nagarcoil from Kochi - you get many trains.
Secondly from Nagarcoil, you get 2790 (Kanyakumari Rameswaram SF Express) on Sunday, Tuesday & Friday @ 10.20 pm night and reaching Rameswaram @ 5.20 am early in the morning.