Hi GrandmaShiela,
Might have some trade for you w.r.t. McNIECE.
There is a nest of them in the area around Glenavy, so just North of Ballinderry.
Conway McNIECE Esq (1738-1811), of nearby Pigeontown, was the brother-in-law, best friend, and executor of James WHITTLE (~1735-~1800) who had extensive linen interests, with international business connections (especially in South America and the West Indies).
However, I don't think this CM ever married ...
----
The CONWAY name is likely to derive ultimately from the major landlord in the area.
[Branding your (usually later) offspring this way was a way of showing allegiance or gratitude in those sychophantic times. Especially if you had just been allocated a particularly juicy farm rental!]
----
The records of Glenavy parish church (St. Aidan's) contain the following baptismal possibilities for you:
19 May 1788 Conway, son of Thomas McNIECE
05 Nov 1792 Conway, son of John McNIECE
And earlier ...
09 dec 1738 Conway, son of Conway McNIECE
----
I'm not aware of any connection with the town of Ballymena.
However, James WHITTLE, and then his youngest son Stafford WHITTLE, lived at Thistleborough in the townland of Ballyshannaghill (Ballyshannochy or Ederaowen) in Camlin parish, a few kms NW of Glenavy village.
This property is referred to as Ballymena in one of the deeds. Maybe your CM was born there ...
----
I have an (incomplete) extract of McNIECE BMD records from Glenavy, assembled by a fellow researcher.
[I am sure he would send you a copy as well.
I'll send you his EMail by PM.]
-----
Interesting about Edinburgh.
The WHITTLEs married LATIMERs who had a presence in Morningside in the mid-19thC ...
----
Y'all keep trawlin' and haulin' there!
Capt. Jock