I apologize for probably raising your hopes that I have information about Ann MORONEY--I don't, but I'm a professional genealogist and would like to offer advice to improve your chances of successful research.
When people read subject lines on a message board, they generally skip over ones that display no information, and continue searching for messages which may be relevant to their search. Subject lines such as yours, or "Looking for great-grandfather from Leitrim" or "Patrick O'Riley", for example, don't give readers with limited time (most of us!) enough reason to open them. People tend to scan the list of messages for something that quickly tells them what they want to know: who, where, when.
Your message's first line already has good information for readers who might have a connection or clue for you! It just belongs in the subject line. Now shorten it, for example: Ann MORONEY/MARONEY b. 1831/2 in Ballina, Tipperary.
By the way, you already use a genealogical convention that researchers greatly appreciate. You put the surname all in caps--plus, you added a slash and the variant spelling!
Good luck in your search for Ann. I hope she "reveals" all those answers to you soon!
Vicki Vaughn, near Seattle, Washington