There is a John Bryson arrived in Portland, ME in 1846, naturalized as a citizen in 1855, in Portland, ME 1855. This John J record indicates he was born County Tryone, Ireland.Maybe you can find a ship arriving on that exact date,and see if County Tryone was actually place of departure. This conflicts with your John being in prison in Scotland! so it may not be the same JJ Bryson at all.He was sponsored by a James Bryson, no further info.
Mary's death cert - viewable online - does list her father as Matthew as well.John's death cert in 1890, indicates he is married - but no other information other than birth in Londonderry.
I wonder where he was in the 1880 census.Not really much help.
United States, New Englan...lization Index, 1791-1906Maine, Massachusetts, New...Bernard) - B626 (Zotique)Image 3913 https://familysearch.org/pal:/MM9.3.1/TH-1-14707-67795-22?cc=1840474 Name: John Bryson Event: Naturalization Event Date: March 30, 1855 Event Place: Portland, MaineCertificate # 1-455 Birth: May 17, 1833 Birthplace: County Tyrone, Ireland Witness: James Bryson,Manasses Ward Date and Arrival Port: June 5, 1846, Portland, Maine NARA Publication Title: Index to New England Naturalization Petitions, 1791-1906 NARA Publication Number: M1299 NARA Roll Number: 52 Film Number: 1429722 Digital Folder Number: 4639028 Image Number: 03913
New Hampshire, Death Records, 1654-19474243488Image 2842 https://familysearch.org/pal:/MM9.3.1/TH-267-11763-147299-26?cc=1601211
Name: Mary A Bryson Death Date (Original): 09 May 1898 Death Date (Standardized): 09 May 1898 Death Place: Bristol Gender: Female Race (Original): W Race (Standardized): White Age: 63 Estimated Birth Year: 1835 Birthplace: , , Ireland Marital Status: Widowed Father: Mathew Kelley Clerk's Locality: Bristol, , New Hampshire Film Number: 1001065 Digital Folder Number: 4243488 Image Number: 02848
New Hampshire, Death Records, 1654-19474243488Image2852
Name: John J Bryson Death Date (Original): 22 Oct 1890 Death Date (Standardized): 22 Oct 1890 Death Place: Bristol Gender: Male Race (Standardized): White Estimated Birth Year: Birthplace: Londondery,Ireland Marital Status: Married Clerk's Locality: Bristol, , New Hampshire Film Number: 1001065 Digital Folder Number: 4243488 Image Number: 02858