Hi Alex,
You may know this but Alexander's parents James Milloy & Margaret Muir were married in Kilmarnock on 11th Nov. 1859 and had 6 kids including Alex.
To find more detail on James the best bet would be a check on the 1871 Census which would tell you which of the kids were still alive, their address at that time and more important, the birth place of James (and Margaret)
Hope this helps,
Graeme
Edinburgh
