I am not absolutely sure that the following will pertains to this particular John Rogers. However, I have tentatively assumed such in entering his date of death and names of family members:
The will of John Rogers of Newport, dated 14 Feb 1714, proved 2 Apr 1716, mentions wife Elinor and the following children: Samuel, John, and dtr. Mary Hamble [possibly Hambley?].
I don't know if any of his children were born of the second wife.
Some genealogies show a son Joseph. There was a Joseph Rogers of Newport who died in Oct 1711, and this may well be John's son (Joseph named a son John; he later settled in Middletown, CT). Joseph had a wife Elizabeth who died at Tiverton, at about 27 yrs of age.