Tylos (Akkadian Dilmun, modern Bahrayn) was indeed part of the broader Hellenistic world IOTL and had some very superficial Hellenic presence, as a part of a very theoretical (IIRC) vassalage to the Seleukids.I think having a Greek colony in modern-day Bahrain or Qatar, perhaps a Macedonian settler colony that increases in population could be a good bet. And if you make them too difficult to conquer directly but too profitable to leave alone, they might be able to survive for centuries as a tributary of whoever dominates the region, most likely Gerrha or the Parthians.
Not sure how you deepen Hellenic presence in the area; the main local written languages seem to have been Aramaic and Hasaitic (the language of official, mostly funerary, inscriptions of the kingdom of Gerrha, possibly to be identified with the "Qatarian" language mentioned by a couple Syriac writers in later times; we don't know very much about it, but scholars tentatively think it may be closely related to Aramaic).