You need to go to
www.scotlandspeople.gov.uk but be aware that you are not allowed to view online any birth certificate less than 100 years ago or marriage less than 75 years ago. You have to order them to be sent to you.
The deaths index lists the death of John Andrews Cole, 28, in 1942.
The births index lists three Cole children, mother's maiden surname Andrews, in Kilmaurs
Agnes McIntosh, 1902
Margaret Matilda, 1912
John Andrews, 1914
and there could be others whose mother's maiden surname has not yet been added to the index.
Thomas Cole and Margaret McIntosh Andrews were married in Kilmaurs, in 1900.
The index to the 1921 index lists in Kilmaurs a household including
Thomas Cole, 45
Margaret Cole, 39
Margaret Cole, 8
John Cole, 6
and in 1911 there are Thomas Cole, 34, and Maggie Cole, 29.
Thomas Perry Cole, 77, died in Kilmaurs in 1952
Margaret McIntosh Andrews or Cole, 75, died in Kilmaurs in 1857
Agnes McIntosh Cole or Tait, 73, mmn Andrews, died in Kilmarnock in 1975
Abraham Perry Cole, 72, mmn Andrews, died in Kilmarnock in 1978
Margaret Matilda Cole, 99, mmn Andrews, died in Irvine in 2012
Agnes McIntosh Cole married Robert Taylor Tait in Kilmaurs in 1927
Abraham Perry Cole married Rosalin Castle Gilliland in Dreghorn in 1929