Hi Linda,
Old Monkland Cemetery was not opened until 1875 and so your ancestors would have been buried in Old Monkland Churchyard, for which there are no records other than monumental inscriptions. The large modern-day cemetery is an extension of the ancient churchyard.
I posted a list of lair (plot) owners for Old Monkland churchyard on this List but having looked through it, I can't see any Irwin/Irvine names. They may not be buried there or, they may have been interred in common ground. The churchyard was open to all residents of the parish, no matter what their religion and there are no separate sections in any parochial burial grounds here in Scotland.