Dear "SBailey,"
The only suggestion I can make is for you to check the volumes of Arnold's Vital Record of
Rhode Island that contain newspaper abstracts. Some of those newspapers MAY have been publishing in the timeframe you are checking.
Incidentally, you can ignore the suggestion regarding the Westerly Sun. The
Utter family started publishing that particular paper in the last decade of the nineteenth century, so it would be useless for your interest in the first half of the eighteenth century.
Hope the above helps! Good luck!