From Bagenalstown Records (Source: Co. Carlow Genealogy Project):
"Mrs. Bryan," to whom Margaret refers in this letter, was probably Mary Coogan Bryan, married to Larry Bryan.  Their daughter Anna is listed in the baptismal records of St. Andrew's RC Church, Bagenalstown as christened in Jan 1820 (sponsors James Coogan and Honor Coogan).  
Another child of the Bryans, John, was christened in January 1823 (sponsors David Tierney and Bridget Coogan).  And Larry Bryan, who wrote to William Coogan from Chicago, was probably the third of their sons.  These listings give as the parents' address Coolnacuppoque.
Mary Bryan was a sister of Mathew Coogan and thus Margaret Coogan Doyle's aunt.  The name Mary Bryan appears in St. Andrew's records on Oct. 13, 1823, as a sponsor (with Frank Coogan) at the baptism of Mathew and Kitty Nolan Coogan's son Patrick.
Margaret Coogan Joyce, married to Michael Joyce, may have been the Joyce "mother" to whom Margaret refers in this letter.  For more about the Joyce immigrants, see Bridget Joyce's letters to her cousins Hugh and William Coogan.