There is a tram/narrow gauge train which runs along the Costa Blanca between Alicante and Denia stopping at Terra Mitica in Benidorm, Altea, Calpe and Teulada (near Moraira) along the way. It also stops at many other stations meaning that it takes quite a long time to cover the route.
At the time of writing this train departs from Alicante every hour. It is probably not the best method of travelling the whole way from Alicante to Denia but it could be used between Benidorm and Denia or any of the stations in between as a novelty.
For more information and up to date timetable and prices take a look at www.fgvalicante.com or phone 900 72 04 72.