Firstly, Golden Orioles breed around Vilamoura and nearby, I would suggest the Parque Ambiental but I can't give specifics except head for stands of tall trees. Of course, keep an ear out for their beautiful song because anyway, that is nearly always the way they are seen as they are real hideaways. Tavira has them too, as Pratincol says. A nice alternative, if you will have a car, is to drive up north-east inland from Vilamoura to areas north of Loulé. I would especially recommend getting up to Barranco do Velho and taking a slow route stopping along the way to Cachopo and then even on to Martim Longo. Golden Orioles are common up there and even found in the villages. Stopping at bridges over streams and rivers is always a good idea too, as they love these inland habitats. A great advantage of discovering inland areas is a whole collection of other interesting breeding birds that are
not on the coast in central and eastern Algarve - along the route I mentioned the following nice species can be found without too much difficulty; Short-toed and Bonelli's Eagles, Rufous-tailed Scrub Robin, Melodious, Subalpine and Dartford Warblers, Iberian Chiffchaff, Woodlark, Thekla's Lark, Rock Bunting to name some. If you get as far as nearly Martim Longo and explore the area - especially river valleys you could even find White-rumped Swift. Then, its only another short drive into the Alentejo and you will be in the realms of many more species - 5 Eagle species, Vultures, Bustards, BB Sandgrouse and many more - but that region deserves more time than a 2-3 hour visit - better 2-3 days.
Another great advantage of these inland areas, apart from being an easy short drive from Vilamoura. is that you will get to see some of the real Portugal, beautiful and vast Cork Oak habitats, charming villages with real Portuguese cafés and eateries - and get away from Golf courses and "Villa-land", which are of great environmental detriment to the Algarve's natural integrity. (excessive irrigation and excessive use of chemical sprays) and habitat removal. Of course, some of the golf courses provide some wetland type habitats (and also land-filled former wetlands!) with some nice birds too but after a couple of days, maybe the wilderness beckons