I have a Joseph Burnside on my line who was born a little earlier in Cockerton, he may be an ancestor of your Joseph, he was a farmer's hind and lived at Oak Tree House, Cockerton in Darlington in 1785 when his daughter Lavinia was born. Lavinia married George Cowley in Haughton Le Skerne, Darlington in 1818 (as Lovehannah Burnside) it's possible they are relatives of yours. However, I have not researched this line yet and the only other scrap of information I have is a grave in Billingham (where the Cowleys migrated) right next to that of George and Lovehannah's son which reads: In Loving memory of Joseph Robert Burnside, youngest son of Joseph and Elizabeth Burnside who died May 9th 1909 aged 23 years, also Elizabeth, beloved wife of Joseph Robert Burnside and mother of the above who died June 11th 1917 aged 65 years.
Although I have not researched this line properly I found the above scrap online on familysearch as a lot of Darlington's parish records are available to view online as scanned images- much more than you get for an IGN search on the same website, if you didn't know this, go to family search's homepage, highlight 'Search Records' and click on 'Record Search Pilot', then click 'Browse our record collections' a map will appear, click on the UK, click on 'English diocese of durham bishops transcripts circa 1700-1900, then click on Durham, you should get a menu which includes parish records for Darlington (which includes Cockerton), Aycliffe, Coniscliffe and Haughton Le Skerne, click on the one you want, then select the time period and click 'view images', it has saved quite a few trips to Durham Records for me and it's nice to view the original records.
Hope this helps,