Have you tried the following site?
http://ngb.chebucto.org/extlnk/lnkframe ... 53A1793777There are Harris's in the New Melbourne and New Chelsea areas of Trinity Bay. I have Harris relatives in the New Melbourne area.
There is a John Harris listed in the Anglican Cathedral , St. John's in 1799. The minister would travel in those days and baptise children listing them upon his return to his home base church.
So you can look around this site i.e. Carbonear, Methodist has a lot of listing who later show up in the Anglican Church and Vice Versa. Are you familiar with the communities and where they are located? If not I can help you, just ask.
Good Luck
Len