On the Family Search Site, there is a christening of a John McKelvie in Wigtown (about 40 miles from Kilmarnock) on 27th August 1807. His father was John and his mother Jean McConnachie.
I am a McKelvie (2 generations ago McKelvey). My McKelvie ancestors came from Ireland 2 generations ago. There was a lot of travel betwen Ayrshire and Ireland in the past, so I don't know if we have a connection.