I see you have also discussed this on Talkingscots.com and supplied a little more information, did you get any answers?
William may have been a member of the Reformed Presbyterian Church but you don't know for sure. If he did belong to that particular church he most probably attended the one in Graham Street, Airdrie which was quite near where he lived. There doesn't seem to be any early records in existence for Graham St, apart from Baptism records 1865 - 1899 which are in the National Archives of Scotland (or whatever they are calling themselves now).
There are records for Gt Hamilton Street, Glasgow but why attend a church so far away when Graham Street was a short distance away?
As for burial places, neither Gt Hamilton St or Graham Street had churchyards.
According to W.G. black's "Parochial Ecclesiastical Law of Scotland" (Edinburgh 1888) page 66
"The right of interment belongs not alone to the heritors, nor to the congregation worshiping in the parish church; all who are parishioners, as resident in the parish, are entitled to be buried there".
so, no matter what faith, if any, a person adhered to, he or she was entitled to be buried in the parish burial ground, so long as that person had lived in the parish.
You will probably find your family in the nearest burial ground to where they lived. Holytown churchyard perhaps? Shotts churchyard would certainly be a possibility. There is a family buried in Shotts churchyard by the name of Lang, from Moffat Mills, Airdrie and one of that family was the minister of the Reformed Presbyterian church at Wallacetown, Ayr. Archibald Lang of Moffat Mills died in 1833, his wife Elizabeth Rodger died 1824. Also, Thomas Lang and his wife Jane Rodger erected a stone to mark their plot at Shotts in 1827.
They may be in Bothwell churchyard but Holytown or Shotts (Kirk o' Shotts) were closer.