some siblings for Bridget from extracted records on FamilySearch :
Honor Folan, 21 Jun 1869, Roundstone No. 2 (district) , Co. Galway
John Folan, 21 Jun 1870, Roundstone No. 2, Co. Galway
Michael Folan, 07 Apr 1873, Roundstone No. 2, Co. Galway
Mary Folan, 20 Oct 1875, Co. Galway
Joseph Folan, 21 Jul 1877, Co. Galway
Anne Folan, 09 May 1879, Letterard, Co. Galway
The parents, Michael and Honor, would have been born before the start of civil records in 1864, so you would need to check into church records for baptisms. The marriage cert should show places of residences for them at the time, which should help figuring out which parishes to start the search in.
Marriages generally took place in the bride's current parish - so Carna is the place to start the search for your Green family, although she may have originally been from somewhere else.