Go to
http://www.familysearch.orgPut in the parents names and click on search.
In the list to your right click on IGI/British
IslesThe result is three births. All after the start of government registration in 1855, so it seems they had not been registering the childrens births with the Church of
Scotland prior to that year. I didn't mention Elizabeth's because you had already listed it as known to you.
You can get a copy of the birth register page for any or all of these births at
http://www.scotlandspeople.gov.uk but the only additional information it would give is the father's occupation and the address at which they were living.
It also means that Andrew and Margaret were still alive in 1861, but not found in the 1881 census, so your search area for their deaths has been narrowed down.