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I did some searching on the subscription site Roots Ireland and found that Edward and Bridget were married in 1850 in the Mayo Abbey parish (see transcription below) which is just to the west of Claremorris RC parish. Cloonshanbo is in Mayo civil parish. They may have gotten the year wrong on the marriage because the first baptismal record I can locate is in 1859 for Patrick and then 1861 for your Mary. There was a John in 1864 followed by Edmond or Edward 1866 Bridget 1868 Peter 1870 Catherine 1872 James 1875 Martin 1876 James 1878 (first James died young/).
The free Irish government site www.irishgenealogy.ie has civil birth records images from 1864-1916. I found the first record available for John in 1864. You can look for records for the other children.
Let me know what questions you have.
Date of Marriage:22-May-1850
Parish / District:Mayo Abbey RC parish
Name:Patrick LorkanDate of Birth:
Date of Baptism:01-Jan-1859Address:CloonshanboParish/District:Mayo Abbey RC parishGender:MaleCountyCo. Mayo
Father:Edmond LorkanMother:Bridget GibbonsOccupation:
Sponsor 1 /
Informant 1:Patrick Lorkan Sponsor 2 /
Informant 2:Mary Lorkan
Name:Mary LarkanDate of Birth:
Date of Baptism:15-Dec-1861Address:CloonshanboParish/District:Mayo Abbey RC parishGender:FemaleCountyCo. Mayo
Father:Edmond LarkanMother:Bridget GibbonsOccupation:
Sponsor 1 /
Informant 1:Martin Gibbons Sponsor 2 /
Informant 2:Mary Gibbons