The forename Nora is likely to be Honora in Irish records. The couple seem likely to have married around 1867. Searching the Irish civil registration records for 1865 – 68 brings up a few possible matches in Counties Cork and Kerry, though there’s the odd one elsewhere. The indexes don’t tell you who they married (you really have to buy the certificates to find out.). However there’s a possible match, from what I can see. Florence McCarthy to Honora Burke, marriage registered in Skull, Co. Cork, 1866 Volume 5, page 813. Someone has listed it on familysearch. You can get a copy of that marriage certificate from GRO Roscommon, and that will give you the couples townlands (addresses) etc with which to search further.http://www.groireland.ie/
Make sure you write the place, year, volume and page number clearly on the order form. And if a photocopy is sufficient, tick that box as it saves money. You have to fax or post the form to them. There’s no e-mail option for certificates issued before 1922.
Tradition was to marry in the bride’s church (which will be on the certificate) and so that’d be the place to look for her baptism and that of any siblings.
You probably need to try and find something from US sources to confirm this is the right marriage. For example a birth cert for any child born there, or the mother’s death certificate perhaps. Either should have her maiden name.
I can see several Florence McCarthy births registered in Skull for 1868 & 1869, any of which might be the son who is 5 in the emigration record.