I found this on the 'net - maybe Rev. Ivers was at the Woonsocket church for a short time... were your ancestors workers in a nearby mill? To verify, I would search "James N. Arnold's Vital Record of Rhode Island" to see where (which town) the marriage record was actually recorded, and then check microfilms of records from that town.
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A REPLY TO DR. BROWNLEY OF NEW YORK; AND A REJOINDER TO REV. MR. DOWLI 1844 Ivers, William: A REPLY TO DR. BROWNLEY OF NEW YORK; AND A REJOINDER TO REV. MR. DOWLING OF PROVIDENCE, ON THE RELATIVE MERITS OF THE PROTESTANT AND CATHOLIC BIBLES. BY REV....CATHOLIC PASTOR OF NORTH PROVIDENCE, RHODE ISLAND. Providence: Benjamin F. Moore. 1844. 120pp. Old institutional rubberstamp at blank base of title page and last page. At top of title page is printed, 'No. 1.] January. [1844.' Bound in later cloth with library markings, Good+. A rare item, and evidently the only printing. American Imprints is the only consulted source recording it. The author responds to a barrage of Protestant "calumnies" against and "slanderous misrepresentations" of Roman Catholicism. Father Ivers's adversaries evince a design "to pick a quarrel with a peaceable and unoffending denomination of Christians, the Catholics of this city, or to excite the religious, and perhaps also the political prejudices of the community here against them!" The pamphlet war occurred at the height of nativist prejudice against Roman Catholics, most of them Irish immigrants. FIRST EDITION