It depends on the time period as to what type of record you will find and what repository the record will be in.
The Methodist churches almalgamated in 1925 so many of their church registers are in the UNited Church of Canada Archives in TOronto. http://www.united-church.ca/local/archives/on/holdings/
1820 is too early for consistent Methodist records.
Based on Barnabas' birth abt 1822, try the Anglican Archives for the diocese of Ontario for a baptism.They are located in Kingston. His father William F. was baptised in the Anglican church in 1797so maybe he was too. Also try them for a marriage record. See http://www.ontario.anglican.ca/archives/
His marriage record would be about 1852 maybe so should have been registered in a civil register called a District Marriage Register but this register for the Midland District is lost. Parents weren't usually named in this time period anyway.
You could also look for estate files for the father WIlliam. Maybe he named grandchildren. Also see if Barbabas had an estate file.
If there are no church records, land records may also be a possibility.
The local Museum and Archives are in Napanee. http://www.lennoxandaddingtonhistoricalsociety.ca/
This is a good website too:http://www.sfredheritage.on.ca/
Other excellent sites to understand the availablilty of records in this period are the Canadian GEnealogy Centre and the Ontario ARchives.