Downings, Killybegs and Caragh all have cemeteries.
Downings is the one previously mentioned (linked by Shane) and was the first church in the area. Killybegs is also an ancient ruined church, in a field behind the road from Prosperous along the canal. It is still used for burials though. Caragh is a separate parish, quite some miles away though, with its own burial ground, still in use.
The RC church in Prosperous IS Our Lady and Joseph, but only dates from the 19th century. There is no attached cemetery. It's at the crossroads, diagonally opposite Christy's pub. The other pub is Dowlings, an easy walk across the road from Christies, on the road to Curryhills.
I think there my be another, more modern cemetery in Prosperous, I will have to check with my husband, as it is his local village.
Will get back to you...
Caroline.