I don't know anything about Applegarths but I did come across this entry in Niagara, Ontario records:
Sarah Applegarth, dt. of William and Martha (Cooley) Applegarth was baptised at Niagara, ONT on 8/11/1816.
Sarah married first Alexander Brown and second George Wells.
Upon further searching I found that William Applegarth was born 1764 in Durham, England and died 1839 in Ontario, buried at Halton Co. Cem.Wife Martha Cooley was born about 1783 in USA.They married in 1811 in Wentworth, Ontario.
Preserved Cooley, Martha's brother, married Catherine Applegarth.
Sarah Applegarth was one of ten baptised on 8/11/1816 in Niagara.The others were all McFarlands or Wilsons (who I believe were related to the McFarlands).It appears that they all shared the same sponsors and witnesses, listed as JOhn WIlson, John McFarland, Eliza and Jane McFarland.
Do you know of any relation between the McFarland or Wilsons and the Applegarths?