If William was the first born child in June 1881, I would assume his parents married in 1880, certainly by Sept 1880.Checking Dyer Co., TN, marriages for about Sept 1880 for a man with surname Canada, I find this:
7 Sept 1879, Dyer Co., TN, marriage of Isaac Canada to Amanda Harris.(Interesting that this man's name is Isaac!)(He was 52 and she was 28 years old.)(Probably not the parents you're looking for?)
4 Apr 1880, Dyer Co., TN, marriage of Robert Canada (24) to Polly Canada (22).
There were many members of the Canada family in Dyer Co., Tennessee.
Since these children were wards and "boarded out" to area families in Dyer Co., there must be court records that you can obtain.I'd contact the Dyer Co. courthouse and talk to the Clerk of the Court and see what records they have.Just might list parents of your grandmother.