Shouldn't be hard to book a taxi at the airport. I've never taken one myself, because I've enough family there, but COK-Alleppey is a standard tourist travel route, and should present no problem. Just get the formalities done inside the airport, instead of negotiating with touts outside. If you're more adventurous, take the cab to EKM junction/south train station and get a ticket to Alleppey (or the other way around) on the shuttle train. Nice views along the route, over the backwater lagoons and close by the beach.