Yes, I should have remembered the Quaker connection + shouldn't reply late at night! - there is a list of known and strongly suspected Manx Quaker families in the paper by Carswell on ManxNoteBook (will also give you some history) - look it up in subject index - however no Looneys are mentioned though most Quakers were from Maughold.
There was extensive emigration from Ulster in the 1720's to North America - there was also the strong link with the Irish and American Linen trade(which I think was strong around Philadelphia) - some early (pre 1700) Manx wills indicate movement from the Island to Ireland in which some named were connected with weaving.