Take the scooter with you in Train when you travel, book it as luggage. Just pad the scooter with some hey and sack, it will be done by the coolies in the train station for a payment, load the scooter in the train in goods carriage of the train you are alighting. Get down in Coimbatore, collect the scooter with you.
This will cost you very little. Fee will be like 1.5 times or so of your travel ticket.
Cochin to Coimbatore is not too far, you can ride it also.