Linda, Below are the AA named Canterbury in the 1880 census who were born in Kentucky.
I hope this will give you a starting point in your genealogy. There are plenty of explanations as to the English surname for an African American, as there are many with Scotish and Irish surnames as well. There are many Africans in the British Isles who may well have immigrated to this country; perhaps they came from Canada.
If your father filled out a Social Security application, you can send for that and it will name his parents; if his parents survived until after 1936, then the same info would be on their applications if they filled one out.
You can search SS Death records at Rootsweb.com to see what Canterbury names are there if your Dad has passed, to see what his # is- if you need that info.
Also, did your Dad serve in the Military? His draft registration would have his SS#, and may name his parents.
Don't give up if you don't get answers right away; keep plugging along and ask questions. See if you can find out if there is a family Bible; check with "older" relatives if possible. You may have to check courthouse records where Dad was born.
If you need suggestions, email me and I'll help if I can. Kathy Abbey