Dockerty/Dougherty Pre 1850

I am trying to find the birth records and beyond of my great grandparents John Dougherty b. 1849 (UK 1851 census age two)

My G/G/GPs Martin, occupation farmer (stated on Johns English marriage certificate)

all I know Is that they are Catholic and come from Co. Mayo.

My DNA shows a 4th cousin in Athlone, Ireland. I have messaged a long while ago but as yet no reply.

Can you help

Everything else I have is speculation because I can’t link them up without john’s birth details

Best regards

Gordon Dockerty