There is no easy direct means of public transport between Alicante to Albuferia by air, rail or bus.
Car hire is expensive and inter-country crop-offs attract a severe premium.
There are no direct low cost flight between Alicante and any Portuguese airports. Equally there is no low-cost flight between Alicante and Seville.
There are also no direct trains.
Your best bet would be to take a bus from Alicante to Seville and then another from Seville to Albufeira.
wwww.alsa.es
has a bus service that leaves Alicante daily at 23.45 and arrive Seville Plaza das Armas at 09:30 the next day.
If you check Cubsur's site at:
http://thomasallen.home.sapo.pt/travel/001.htm
you will find the timetable for Damas services from Seville to Albufeira.
There is a departure at 1615 arriving Albueira at 1940.
Short of major dogslegs via Madrid and Lisbon this is the only direct route by public transport.
