Barb,
I have been collecting as much info on Hay names in Ayrshire...mostly by replies on this site for the past few years. So most have not been thoroughly researched and I can't attest to authenticity. What I do have is John Hay born ~ 1767, died 1836, age 69, buried in Tarbolton, occupation-shoemaker. Married Margaret Drinnen who died feb 1869 age 98,buried in Tarbolton. I have a list of suspected children including Janet c 30 June 1799 Tarbolton. Not sure of any of this but it might give you a lead. Let me know if this helps or if you have any other Hay data to share.
best luck
dale cook