I've just spent a goodly amount of time looking for this information. I see Deliverance Peck (once Deliverance Swanson Peck) all over the internet. But of course there are no sources listed. Supposedly she and William married 26 June 1662 in Swansea or Newport RI. A specific date would indicate an actual marriage record, but searches in several databases for Deliverance Peck and/or Swanson in Rhode Island and Massachusetts did not find this record. Torrey's New England marriages, which is pretty good at ferreting out marriage data has this:
COHOUN, William1 (-1675) & ____ ____; by 1670(1?), by 1665?; Swansea {Cahoon 41; Sv. 1:328; Reg. 52: 148; Cahoon 17} Savage lists only that William was of Swansea, no wife. Reg 52:148 seems to be an error. The other reference Cahoon, Ida M., History of the Cahoon Family (Cleveland: W. A. Robertson, 1912) is available at Family History Libraries. But it doesn't list a wife or her name would be in those blank lines.
I have found no reason to believe in Deliverance Peck at all and she wasn't listed in the will or birth records of the parents listed on her profile.