Agnetta,
The name McAllister[ two l's] does appear in Down, whether from records I don't know, but Elizabeth McAllister was my Grandmothers mother, born in Newtownards around 1855. She married Thomas McLennaghan, and they had five children that I know of that initially settled in Scotland...... Ellen [ Nellie ]McLennaghan married Sam McTear. Annie....married a Johnny Mackin and lived in New Lanark. Margaret[ Maggie]...married a White and also lived in New Lanark. Elizabeth...married Andrew McTear and lived in Carmyle near Glasgow. Johnny....lived to 107 and settled eventually in Ontario with 10 kids. The McTears and McLennaghans also came from Newtownards in the 1800's. Sorry, can't help with the rest.