The parish on Miscou is St-Antoine de Padoue (St-Anthony of Padua).
Here is a link to the names of the parishes of the Diocese of Bathurst, NBhttp://www.gcatholic.org/churches/local/bath0.htm
The closest parishes to that were Lamèque, Shippagan, Caraquet and Inkerman. One often finds records from Miscou in the registers of Carleton and Bonaventure, QC.
Before 1822, the only parishes I can think of that were around were: Carleton, Bonaventure, Bathurst (Ste-Famille), Petit-Rocher, Néguac and Caraquet, and possibly St-Jean-Baptiste, Tracadie. Most of the other parishes in the area were missions of these churches, and founded towards 1850 or later. Hope this helps.