There is certainly no train service. There are no direct buses either.
The nearest town to Islantilla with a substantial bus service is Lepe, the "strawberry capital" of Spain and about 20km east of Ayamonte on the old Ayamonte - Huelva Road..
I have checked on the Spanish web and while there are indications that DAMAS, the local bus company operate between Lepe and Islantilla,
This schedule might work but is convoluted:
Faro Airport to Faro Station - Taxi or Bus
Faro Station to Vila Real Sta. Antonio Station - Train (The Damas/EVA bus to Ayamonte/Seville times do not tie in with this schedule unfortunately as there is no corresponding bus between Ayamonte and Lepe.)
Dept. Faro: 14h34
Arrive VRSA: 15h41 (16.41 Spanish Time)
Walk 1km to the Ferry over the Guadiana (Add one hour for Spanish Time)
Ferry to Ayamonte and 1 km walk to the Bus Station Bus
Dept. Ayamonte 19:00
Arr: Lepe: 19:15
Taxi 7kms to Islantilla.
or: (just found this link)
The Lepe Council (Ayuntamiento de Lepe,) have just announced on their website that there will be a bus running every 30 minutes from Lepe to La Antilla and back from 07:00 to 24:00 throughout the summer. Islantilla appears to be on the route into La Antilla, which is the local village.
See: http://bit.ly/aIHt25
Remember it may be quite hot at the end of August and walking between the Station with baggage is probably not what you want.
The alternative is a transfer with one of the myriad shuttle companies operating out of Faro Airport, such as http://www.low-cost-transfers.com/faro-airport/index.php
