To add to Hugh's information, if you consult the 1911 UK Census (Scottish Section) on Scotland's People, there are two persons of those Names or variants, LIVING in AYRSHIRE, in the expected Age Range.
I actually used for the Age Range, of being born from 1900 to 1911 inclusive, AYR(shire),
This produced two results, one aged 2 and the other 4.
I did not attempt to isolate to the Registration Districts - too many; but if you buy some Credits, you will get quite a wheen of information, including probably Where Born.
If you follow through, you should be able to get more details of their respective families.
Assuming that one of them is the person you seek, you should be able to make relatively rapid and cheap progress to earlier generations on Scotland's People.
For earlier than about 1881, you may also find the LDS Family Search siteof use-