The only church dedicated to St Ninian in Westmorland, so far as I know, is at Brougham and in fact this is the only one in the whole of Carlisle Diocese. When you say you have contacted the church, is it the one at Brougham.
St Ninian's, Brougham, or more correctly Ninekirks, is now redundant and is extremely remote i.e. you have to park, then cross about seven fields on foot before coming to the church on the banks of the River Eamont.
If this is the church then the newspaper that covers that area is the Cumberland and Westmorland Herald or the now defunct Penrith Observer. The Westmorland Gazette covers South Westmorland.
Names would help.