Leighton and Ferguson help please

[L L]

I have hit a brick wall and would greatly appreciate any help or advise.  I have been tracking my ancestors in Scotland and then was surprised that they came from Ireland.

I have Thomas Leighton(Lighton on the 1841 census) who was born abt 1792 in Ireland and died 4 Jul 1857 Ayr Scotland.  Thomas Married Elizabeth Wark b abt 1793 Ireland d. 21 Mar 1864 Kilmarnock, Scotland.  They have the following children:
Jean b. abt 1822 Ireland
Mary b. abt 1824 Ireland
Joseph b. abt 1828 Ireland
Elizabeth b abt 1832 Ayrshire, Scotland
Thomas b. abt 1836 Ayrshire Scotland

From this I am guessing they moved from Ireland to Ayreshire between the years 1828 and 1832.  I believe that Thomas's parents were Thomas Leighton and Jane Ferguson.  I also believe that Elizabeth's parents were Henry Wark and Elizabeth Kid.  Not sure how to even go forward with this as I have no clue where in Ireland to even be looking at.

Lydia