Well, there are many versions of this song, so the Digital Tradition has given it a number, #320 to link the various versions. A search for #320 (click) brings up "Butcher's Boy," and another song that you may find surprising. A search for [wide and deep my grave shall be] brings up an interesting parody that Dick Greenhaus had a hand in writing, which means there's a good chance that Greenhaus might remember the original. I'll send him a personal message and see what he can come up with. The man has more songs in his head than he has in the database.
The square brackets in the search above limit the search to a specific phrase. If you skip the brackets and just put grave wide deep (click) in any order in the search box, you'll get all the songs that have all three words, and you will see that deep, wide graves are a recurrent theme in folk songs, and this could lead to a discussion of morbid attitudes among folk singers....
It will also lead you to a number of songs that are related to the one you are seeking.
-Joe Offer-