Just came across this thread since you posted under Antrim Resources & Offers (which isn't for queries) rather than the main Antrim board. Just click on 'report to moderator' and ask for it to be moved to the correct board.
Are you very sure that Andrew Boyd & Elizabeth McCulloch were Catholic/would have been married in a Catholic ceremony? McCulloch (McCullough & other variations) can be either Catholic or Protestant but Boyd is more commonly a 'Protestant' surname (strongly Presbyterian).
Unfortunately the dates you are looking at are very early for church records of any denomination so it may be impossible to find any trace of them in Ireland. Have you considered that the son John Boyd might have gone to Australia with a relative or perhaps either joined one there or had relatives join him?
'Ballymena' covers a fairly wide area, by Irish standards at least, and most of that area is rural. It wasn't uncommon for people overseas to give the name of the nearest large town as their homeplace rather than the townland where the family actually lived.
