apply new one under LTF and close old one (through twitter or mail, if you have payslips above 50k).
You can have multiple Corals at the same time (crazy things at ICICI) under one account itself.
Note: AFAIK, In ICICI if you take any paid cards its very difficult to convert to LTF.
You can close the card by speaking customer support, if they're in good mood can listen your reason and arrange a call from retention team or offer LTF on the spot, else they simply take your closure request and process in 7 working days (RBI Watches in this period), try at your own risk.
If you don't want to loose CIBIL, take platinum card under LTF, close Coral, and apply Coral LTF (all happens in one CIBIL account without loosing credit history).
Branch people won't help you because low MAB.