I found 3 children born to William & Martha in Ireland:
Here’s James birth in Kilknock which is about 3 miles north of Randalstown.
There are no migration records for journeys to Scotland. It was (and still is) just a short domestic journey. So you will be reliant on when they first show up in Scottish records, and that’s about as close as you’ll get to knowing when they moved.
This looks to be James Galloway in Kilknock in the 1901 census:
According to the Valuation revision records they lived on plot 12b which was a labourers cottage.
Family in 1911:
James died in 1920:
I can’t see a death for Margaret though it was evidently after 1920. The Valuation records stop in 1929 but they indicate there was still a Galloway living there then.
Birth registration only started in Ireland in 1864. I can see 4 children born to James & Margaret 1864 onwards:
Un-named female 22nd July 1864
Un-named female 11.9.1872
Un-named female 27.2.1875 (who may be Agnes going by her age in the 1901 census):
In the early years of birth registration it was common to register a child’s birth without a name. (In most cases the parents hadn’t decided on one).
For births prior to 1864 you need to rely on church baptism records. Nearest Presbyterian church to Kilknock is probably Grange in Taylorstown though folk didn’t always attend the one closest to where they lived. (There are 3 Presbyterian churches in Ahoghill, 3 in Randalstown and another at Craigmore). Neither the Grange nor any of the other churches have their records on-line and so you would need to get someone to look them up in PRONI in Belfast. If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
The baptism records may also help identify the 3 un-named births post 1864.
Belfast Telegraph of 26.10.1967 reports that a WJ Galloway, aged 67, of Kilknock, Randalstown was seriously ill in hospital after a collision at Kilknock where he was knocked off his bike. Presumably some sort of relation?