I have Sullivan's from Co Monaghan in my family.. from my grandmothers side in fact my middle name is Sullivan.
I don't have much to go on either but you can see if any of the names ring a bell, here goes -
James Sullivan born Antrim married Mary Small Monaghan children Bernard, Con, Ann, James , Mary, Alice, John all born Monaghan.. family moved to Scotland around 1849-1850 but no wife Mary with them.
James re-married in Glasgow and had more children here.