I have traced my Coulter line to the Ards Peninsula in County Down, Northern Ireland to the late 1700's although I suspect they may have originally come from the other side of Stangford Lough.
The earliest Coulter reference I can link to is for a James Coulter of Ardkeen who is a Church Warden at Christ Church of Ireland, Parish of Ardkeen, Diocese of Down. The reference is found on page 107 of the book Diary of a Country Parish: Christ Church - Ardkeen Diocese of Down by Rev. Cannon Frank W.A. Bell, M.A., B.D., circa 2001.
By the mid 1800's branches of the family are farming in two distinct areas: Dunavely (and the adjacent townland of Broom Quarter) and Granagh which lies just past Portaferry near the tip of the Peninsula.
Although listed as Presbyterian in later census, the Dunavely branch of the family was active in Christ Church, Ardkeen Parish, Church of Ireland while the Granagh branch attended Portaferry Presbyterian.
My Coulter line lived and farmed in Dunevly and Broom Quarter next to Ballyfinragh Lough for many generations. Interesting video of the rath and surrounding area.
Marriage records that I've gathered. Some are 'my' Coulter family but there are also families that I am not related to. Please note that this is a work in progress. I will be adding and updating.