I looked at www.rootsireland.ie for Mary Bligh 1806-1826 and found 3 possible records. I have used a wide parameter for the date range as it has proved time and again that dates can often be incorrect. Most people who left Ireland were illiterate and undocumented. They had never seen their names written down and had no clue as to their date of birth. Often these were guessed when boarding ships and entering ports. So it would be very wise of you to keep an open mind.
the 3 records are as follows....
Mary Bligh baptised Feb 1817 address not recorded parish/district Castlerea Co Roscommon denomination Roman Catholic
father John Bligh mother Mary Flinn
sponsor James Bligh and Ann Flinn
Occupations were not recorded.
Mary Bligh baptised 5 July 1826 address not recorded parish/district Roscommon Co Roscommon RC
father John Bligh mother Margaret Feehily
sponsors Francis Mc namara and Elizabeth Bligh Again occupations not recorded
Mary Blygh dob 11 Apr 1806 address not recorded Parish/district Castlerea Co Roscommon RC
father John Blygh mother Anna Frein
sponsors Patrick Waldre and Eleanor Mannion
I dont know if any of these are your ancestor as it's impossible to determine without having the parents' names, but I hope this small bit of information may help you in some way.
I think that it may be worth exploring military records. The name Bligh (Blygh) is not too common. The English National Archives has more that 800 muster books and pay lists of Irish county militia and volunteer regiments, WO13/2574 3370 dating from the end of the 18th cuntury to the late 19th century. Musters may also show enrolment and discharge information. GOMs 608 has 1761 militis lists for countiies Cork, Derry , Donegal, Down, Dublin, Kerry, Limerick, Louth, Monaghan, Roscommon, Tyrone and Wicklow.
So sorry that I can't be of more benefit to you,
Good Luck in your search,