Henry Joy McCracken is definitely by PJ McCall. He based it on a song common on Ballad sheets "The Belfast Mountains" and it was published in "The Shan Van Vocht" a monthly periodical edited from Belfast by Alive Milligan and Ethna Carberry. I don't have the issue number or date by me at present.

I have no idea who wrote the other song, more often called "Henry Joy." Robert Cinnamond had it (being recorded about 1958) but I remember it suddenly arising in the Belfast of the middle sixties and I have never been able to discover whence it came.