There were a few hundred "Moravians" in Dublin in the 19th century, but they were all English and Irish - they belonged to the Moravian church. One of their churches, in Harry Street, was turned into a pub - McDaids. The old stained glass windows are still there. Their preachers travelled around the country, but politics crept in (alway does in Ireland) and they split into different sects and eventually faded away. Unfortunately don't know anything about their music.
More about the Moravian church here.