Hi Jim
I feel the next step would be to obtain Hugh and Martha's marriage cert. as in message 2 as this should confirm his father's name. Otherwise we are only guessing, and we want to be certain of our facts before delving further back.
One thing I do know is that the Converys originated from Co. Derry.
Let me know how you get on and I will be happy to pursue the search further.
Marian
Manager